The weather should be very nice in November. I'll give you a few ideas to get you started and I'm sure some others will add some things to do.
Beach- Go to Siesta Key. It is always voted one of the top beaches in the USA.
Restuarants & Bars- Try downtown Sarasota. Lots of good places to go.
Walk Around + Restaurants-Go to St. Armands Circle. There are some good restaurants and a lot of stores. The Tommy Bahama restaurant is excellent (expensive too).
If you want to go to an old Florida style restuarant that has great fish, try the Casey Key Fish.
http://www.caseykeyfishhouse.com/fishhouse.html
Have a good time.