Late April to early June is an excellent time to visit. the weather is usually great here then - it can get very hot later. It's also before the peak of the tourist season, although there are always some tourists visiting.
I use this site for hotels here in Italy:
http://www.venere.com/italy/florence/ Personally, I like to stay in the area around the Duomo when I stay overnight. However, the old town is pretty compact and it's very easy to walk from anywhere between Santa Maria Novella station and Santa Croce. Places around the station tend to be a little cheaper if that's a major consideration.
A place I particularly like is:
http://www.venere.com/hotels/florence/ho… , but there are many good places to stay.
When you're in Florence, it's a good idea to make reservations for the Academia and the Uffizi if you want to go in. You can avoid the long lines to get in. there's a ticket booth on the back side of the Orsanmichele that rarely has any line where you can get tickets to the museums. If you go up to Piazza Michelangelo for the postcard views looking out over the city, be sure to continue a little further up the hill to San Miniato al Monte. The interior of the church is very nice and the small shop run by the monks is good.