Can I suggest an apartment in Rome? The Trastevere or Piazza Navona areas are convenient, by foot or tram or bus or taxi, to the Vatican, Forum, Pantheon - just about anywhere for the first time tourist. But the nights in Trastevere are very special. Great street performers (especially at Piazza Santa Maria in Trastevere), food (around the same area) and people watching (yep, same area). I would not say it is 'touristy' but rather this seems to be more like a real Roman neighborhood. After many years (this will be 15 in a row) in Rome, I find myself in Trastevere almost every night during my week or more visit. For 5 people it should not be hard to find an apartment with enough bedrooms and bathrooms to keep everybody comfortable.
I'd say Florence is going to be a bit more of a challenge. RS has good recommendations for hotels. Sorry, even for a few nights I rent an apartment (a clothes washer does come in handy!). 2 nights? Oh my! That's really only 1 full day. Florence, during the summer, is crowded. Which means long lines. But Florence is also a great home base for day trips to Siena (amazing), Lucca (charming) and even the Cinque Terre (great sea food and walks). I wonder if you could get more out of your first trip with fewer travel days? No matter what you do, I bet you'll be planning your next visit while you're on the plane going home!