We have 4 nights in Florence. One day we will take a tour of the country side for sure, not sure of other days. I'm not a huge art fan but will go see David etc. My husband loves the idea of being able to walk around cobblestone streets and visit with the locals. We also like shopping, dining, etc. Our budget is $100 USD per night. There will be four of us so either 2 rooms at a hotel or an apt with separate bedrooms. Any suggestions?
Your price will greatly depend on when you go. During the summer months, prices will be higher. Is your budget $100 per room per day? If so, then you might be OK. There are a lot of options for doubles or even quads. I recently stayed at the Hotel Accademia and was pleased with its central location. I have also stayed at the Hotel Loggiato dei Serviti and was impressed with it, but it is probably above your budget. you might try booking.com as a starting point to see what's there and the availability for your travel dates.
Asking for suggestions on "what to do", "which area to stay", or "specific accommodations". For what to do, any search on the top attractions in Florence will give you plenty to do for 3 days. A lifetime is probably not enough to see everything there is to see in or around Florence. I've lived there most of my life and still there are things I haven't visited yet. For which area to stay, if you don't plan to have a car (you don't need one), you should stay in the Centro Storico (historical center). Anywhere in the Centro storico will work and you will be within walking distance from everything. Florence is very safe, probably even more so than Redwood City, which is also safe (I work in your town). For accommodations, Booking.com, Venere.com, or also homelidays.com or homeaway.com for apartments, will yield plenty of choices. You won't be able to find 2 rooms at $100 total, maybe $100 each (although 100 Euro per room is more likely). You might be able to save with an apartment with two bedrooms, rather than 2 hotel rooms. Check Homelidays.com or Homeaway.com (affiliate of VRBO.com). Lots of apartments however, may not be in the Centro Storico, therefore check the exact location. Try to be within 1 km radius from Piazza della Signoria if you can. http://www.freemaptools.com/radius-around-point.htm In Search Box enter: Piazza della Signoria, Florence (click search) Zoom in until you see Piazza della Signoria
Below the Map, Under Options enter in the box Radius Distance: 1 km. Click on the map on Piazza della Signoria Make sure your hotel/apartment is within the green circle (or very close outside). Anything within a 1.2 km circle from Piazza della Signoria is still Centro Storico. South of river may be cheaper.