Buongiorno,
I suggest you start by reading this article which lists a combination of places to stay both within the city center and just on the outskirts.
http://www.visitflorence.com/florenc...ten-picks.html
Also have a read through these articles which highlights different activities to do with kids (some are in the city center and some are outside the city center)
https://www.discovertuscany.com/what...fun-with-kids/
I also suggest that as you select the museums for the adults to visit that you check out the “kids itinerary” - for example Fiesole has a family itinerary that you can pick up at the tourist office that will introduce you and the kids to this amazing city only a 10 min bus ride from Florence with Roman ruins and parks for hiking: http://www.familytour.it/en/fiesole-family-tour-en.html
Buon Viaggio,
Donna Denise
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