Our free time in Rome was spent walking around. The first day we just walked around and found the Trevi Fountain and Spanish Steps (which were also part of our tour the next day). In the evenings, we walked around and ate at little cafes and saw the Trevi Fountain at night. On the one afternoon, we found a Steelers bar in Rome and had a couple of drinks there and then walked back to our hotel. You can also take an open air bus tour through Rome (and I believe you are still provided a free pass for this by ABD).
In Tuscany, instead of relaxing at the resort, there were 21 of us that did a trip on our own to Pisa. It was quite the adventure. I am thrilled that I got to see The Leaning Tower of Pisa, but I have to be quite honest, I don't know if I would do that again if I had the choice. The guides can help you with the arrangements, but that is it...the rest is on your own. In Florence, if you like to shop, this is the place. Leather is of the highest quality and you will pay less for a high quality leather coat in Florence than you will pay for a cheap leather coat in the US.
In Venice, there wasn't enough time to actually do a trip to Murano (unless you are staying extra days). We just walked around Venice and enjoyed it uniqueness and beauty. I wish I had extra days in Venice as I just loved it. Walking around in Venice, getting lost, eating in one of the many many restaurants while people watching. The guides will give you plenty of ideas of things to do on your own.
It's a fabulous trip and you definitely get to see lots and lots of things via the tours, but just walking around and people watching is half the fun for us.