In Florence, some of my favorite places to eat are -
La Terrazza Del Principe (http://www.laterrazzadelprincipe.com/index-en.html) It's on the Oltr'Arno (other side of the river) up the hill towards Piazzale Michelangelo, so you'd probably need to cab or take a bus, but it's worth the trip. The views are spectacular, the food is amazing, and the owners/staff are incredible. It's a really special, totally non-touristy experience. Reservations recommended.
Acqua al 2 (http://www.acquaal2.com/) This is a little bit more "touristy", since they also have locations in the US (San Diego and Washington DC), but it remains an amazing restaurant. Get the bistecca al mirtillo (steak with a blueberry sauce - sounds weird but just trust me) and the fusilli lunghi al mascarpone e funghi (pasta with mascarpone cheese sauce and mushrooms). Reservations recommended.
Mercato Centrale (http://www.mercatocentrale.it/en/mercato-centrale-firenze/) This is a two story food market where you can buy great supplies for a picnic, souvenirs to take home, a cheap panino, or groceries to cook on your own. It's also a sight in and of itself - just be respectful of the people doing their actual grocery shopping there :)
As far as getting around in Florence, it's best done mostly by foot, unless you take a cab/bus up to Piazzale Michelangelo. The city is extremely walkable.
In Rome, my husband and I found it EXTREMELY worthwhile to get the Roma pass. Not only did the pass make financial sense for us, it was worth it JUST to skip the lines at the Colosseum. Even in January, during "low-season", the line for the Colosseum was over an hour long. With our passes, we waltzed right in - no waiting whatsoever. Also, the pass included free use of public transportation (both buses and subway), which made it a no-brainer for us. We opted not to purchases museum passes in Venice and Florence. We did buy the Vaporetto pass in Venice and it saved us a ton of money; we qualified for the "Youth Pass" (20 Euros for unlimited 3 day travel), but I think it would have been worthwhile even at the full adult rate.