So I'm from Europe and have now done 2 Med cruises with
DCL with 2 more this summer.
Even as a European, it's rushed. You only have 1 day to visit each city and there is so much to see .. honestly, if you like your sight seeing and history, then Europe definitely has it in abundance.
Saying that though, it's a great little 'hello' to Europe and well worth doing, if only to know you want to come back maybe?!
One thing I would say, is that organising your own tours allows you to see much more of the cities IMO. We did a mix of DCL ones and DIY ones last year and the DIY ones were by far better.
For Rome, we had mini vans which could get right into the city centre .. DCL had coaches/buses which could not, which meant all passengers did a great deal of walking that day (100 degrees!!!)
Some DCL trips may be better, but from what we heard from fellow cruisers there was alot of walking, waiting for everyone to gather, then rushing to the next bit.
There's a great thread going for Med cruisers this year (any date) .. gives lots of info about booking things DIY and how people got on.
Med Cruisers Planning Thread
Although ideal to fly in the day before, we never have and we've been ok so far (touch wood)! If you book DCL transport, at least they'd be someone waiting for you at the terminal .. it's not far to the Port. I'd pre-book a cab for the return journey though to save money.
For jet lag, try Melatonin. It's great and something we always pick up when we're in the US at Walmart.
Hope that helps .... fingers crossed we'll be welcoming you to Europe soon!
p.s. Did you realise that DCL are most probably coming back to the Med in 2014 too? Port schedules suggest that they'll do a few Med cruises, then up to the Baltics (sail from Dover, England ... near me!!), then back over to the Med again.