Sheraton Firenze is far outside the city, it's practical to visit The Mall but there is basically nothing around (nice landscape though, which will be lost on teenagers I expect).
Other Firenze have jumped to Cat 6. so they are not involved in the Inspirationnal Award anymore. By all means go there. They are facing each other just by the Arno (the river).
The Sheraton Roma is a good hotel in a nondescript area (basically a motorway near the airport). The shuttle is free to go to the center and back, but of course you won't have the possibility to rest during the day because the hotel is too far.
The best Cat 6 Roma hotels option is IMHO the Eden. Be prepared to spend a fortune though.

I hope this helps,
E