Because I know some people need the information almost immediately, here's our take on doing the ports
ON YOUR OWN. DW and I are 32 with no kids, and definitely active.
Barcelona: Up to you whether the taxi to/from the airport is worth it. Trip back cost us 37euro due to 4.20 airport fee, 4.20 port fee, 2.00 for bags, and the ~26euro fare. On the way in at the beginning we took the train, and the 10 trip card that we used for it (~10euro, can be split amongst a pair/group) was also good for all our Barcelona touring. Metro is very easy to navigate, like any other city figure out what stop you want, which line that stop is on, and what direction you need to travel on that line to get to that stop.
Villefranche: Tendering is always a pain, so tough to schedule things exactly if you're doing things with set times. We weren't, so we came off when tender tickets were no longer required, and still had plenty of time to do both Eze and Monaco. The trains here are the same concept as the metro when it comes to navigating. For us it was either towards Monaco, or towards Villefranche. Buses (the only way to get to Eze) were a bit more challenging as the driver had a lunch break in the middle of the day when my wife was trying to catch one, so make sure you're monitoring the schedules. I hiked the trail up to Eze as part of my long run, and it's definitely no joke going up (1200 feet vertical in 1.25 miles, took ~30 min) but many people take it down to connect up with the train and skip the bus down. For Monaco, when you get off the train take the escalator up, turn right across and above the tracks, take the escalator down (none of the signage is too helpful yet) and make a left U-turn to go out those big side doors towards the sunlight. From there you'll see casino signs but it's basically up the hill sloping away and to the left. Come back into the station through the same door and you'll want to stay on that side of the track to head back to Villefranche. Using this path we had minimal climbing or elevation change, but to see other sights in Monaco you might have much more. Also, at the all aboard time there was still a huge line for tenders, so don't panic.
Civitavecchia: It is most likely a LONG way from where the cruise ship parks to the port entrance by the fort (we ended up at the furthest spot, which isn't immediately clear from onboard). We power-walked the 1.5 miles. Don't. While the free shuttles weren't running yet and that was the fastest way to the train station, it was only by a matter of minutes and probably not worth it when you have a long day of walking ahead. Right as you go through the gate after the fort up onto the street, there is a helpful desk where you can buy your BIRG tickets. No line (because again we beat all the buses) and we had our tickets and were off in about 10 seconds. We made the ~8:03 train, which then sat in the station for 10 or 15 min for some reason. That put us in Rome and at the Vatican by 9:30. Our tickets were for 15:00, because we'd read you can enter early but not late. This was NOT true as they turned us away and said we could come back 30 min prior but not earlier. The line was literally around the entire Vatican City at that point in the day in the blinding heat. We swapped up our itinerary to do the east half of the city first instead. Metro to Spanish steps, and did that, Trevi Fountain, Pantheon, Victor Emmanual monument, Forum, and Colosseum in quick sucession. All walkable (with a map) and very little transit time between each. Metro back to Vatican, and greeted with much smaller crowds in the afternoon. Did that, used the "secret exit" between Sistine and St Peters, and were back at the St Peter's train station in plenty of time for one of the last trains, and in fact saw all the tour groups get on their dedicated train five minutes before ours. Total transit cost 12euro each for our BIRG tickets, big time savings.
Piraeus: It's a short walk from the ship out to the port entrance, the very first bus stop is the 843 to the metro. You can buy your ticket for the bus across the street from it at a little booth labeled bus information, and it was something like ~1.40euro, allowing you to transit on both bus and metro for up to 90 minutes or something. We took the bus a few stops down to the train station, which is at the end of a line, so you just get on and wait for it to leave a couple minutes later. We chose to get off at Thissio, because it was on the convenient side of the Acropolis to where we were going, and required no transfers (the Acropoli station requires two transfers). We were walking up the hill to where we were meeting our bike tour by 9:00. The sights are all pretty compact and walkable, and later in the day we got back on at Syntagma, which required an easy transfer back to the green line to terminate in Piraeus (again the last stop, impossible to miss). Same bus back (remember your metro ticket counts as your bus ticket as long as you're still inside the time window) and the quick walk to the ship. Total transit cost 2euro and 80 cents each. Again massive savings. Some of the sights we did do have entry fees (Acropolis/Parthenon/Temple of Zeus, Acropolis Museum, Panathenaic Stadium) so make sure to add that in to your budgeting.
Kusadasi: This was the only port we chose to take an excursion. Part of the reason is everything would have been taxis, as there is no public transit to some of the sights we wanted to go to like the House of the Virgin Mary. Once we added up the predicted taxi fares, it really wasn't that far off what Disney was charging. The other reason is we had become fast friends with some of our table members and they were doing it, so we tagged along. We did the Best of Ephesus, which did Ephesus, House of Virgin Mary, Cathedral of St John, and then a massive buffet lunch at the waterpark. If you add up the entry fees, figure out a cost of a buffet, and then add up all the transportation (port to Mary, Mary to Eph, Eph to StJ, StJ to food, food to port), it probably would have been close to the $99/person Disney cost. So sadly, not a lot of money saving tips here. Our other bonus is we won the $200 onboard credit at the DVC members gathering, so we just spent it on this.
Mykonos: Free shuttle from literally a few feet from the gangplank into town. A few feet from that is a place that rents scooters and ATVs. 15euro for the day for a
scooter, 25 for an ATV that has reverse gear, and boy are they fun if you're headed out to the beaches. They kept our drivers licenses (US ones are fine) and we were soon zipping out to some of the more remote beaches. If you want one that will probably be deserted at the end of a road that goes from paved to dirt to bumpy that's off the beaten path, try 37.425495,25.304716 in Google Maps. If there are in fact people there, and they are both unattractive and naked (you never know, but we were unlucky) then you can double back to Agios Ioannis which is the one you saw just around the corner with the umbrellas, which is also nice. Wind direction is also key, for us it was out of the west and pretty strong so the hidden beach was getting a bit more peppered than the south facing beach was. Returned the scooters in plenty of time, caught the free shuttle back after wandering around town, really easy.
Valleta: This one was a bit more challenging, namely because the main attraction of the Blue Grotto is on the far side of town. Walk up to the main Bus terminal area (or take the elevator a block or two further towards town, which will require some doubling back and is 1euro/person) and figure out your plan. Our schedule that I brought did not match what they were actually running (which was labeled as November 2012 holiday/winter schedule by the way), so tough to preplan times. We took the 71 to the 201 transferring in Zurrieq, but the 201 is only once an hour and we showed up with 40 min to kill in Zurrieq. Took that to the Blue Grotto, and the way the times worked out once we were done with that we caught the earlier 201 outbound, got off at Haqar Qim, wandered a bit, and still had time to catch the other 201 bus inbound, running back into the same people at the Blue Grotto who had stood there waiting the entire time (in the heat). The 201 bus seemed to constantly run late, so continuing on to Dingli cliffs or Mdina is something we passed on, mostly due to cumulative fatigue from the rest of the trip. Once an hour in peak summer tourist season seemed pretty subpar planning by the bus people. The 71 bus from Zurrieq was running like every 10 minutes, but the 201 bus we were on actually continued on to the airport first before doubling back to Zurrieq, so we hopped off at the airport and transferred to the X7 back into Valleta. Clear as mud? While a pain, again an all day bus pass was 2.60euro/each, and that was out only transit cost of the day. Also, PLEASE skip the Malta Experience, unless you want to watch a 35 minute not even good enough for the history channel documentary on Malta. We thought it was something else (45 minute 3d walkthrough we'd read about) and it definitely wasn't. At 10euro/person it was a total rip off and the only thing I regret doing on the whole cruise.
Return flight: We walked off the ship at 7:20ish (with no line) grabbed a taxi (with no line) ended up paying the 38euro + tip mentioned earlier, got to the airport by 8:15ish, checked bags, were through security and passport control by 8:30, and were sitting in the lounge waiting for our flight to board shortly thereafter. Our 10:45 flight supposedly started boarding at 9:45, but it was closer to 10:00. As we passed the passport control lines they did look like they had gotten gnarlier around the 9:30 timeframe. So yes, can EASILY make a 10:45 flight out of BCN. Could have saved money on the taxi by doing shuttle to metro to aerobus, but we were hauling bags and that would have been painful.
Questions? 
but I really can't remember) In the pack they sent to me here in Greece there were also two tickets for entrance that I am free to give away to whomever I choose. 
I just remembered, I think the cards also get admission to the museum at parc guell! The deal was just too good for me to pass up. To be honest, if in the end we are not able to get to any of these places, I still will feel that I have contributed to the building fund. 
so, yes, I think it is totally worth it
in my 30's with kids. Kudos to you. I know we're the same age-ish but can I just point out that you have an IRON MAN icon in your signature. 
