I've spent a bit of time visiting my cousin in Sarasota. Some of the things we've done around there are:
Ringling Museums -
http://www.ringling.org/
Marie Selby Botanical Gardens -
http://selby.org/
Myakka River State Park -
http://www.floridastateparks.org/myakkariver/
We've done the sightseeing cruise around Sarasota Bay -
http://www.lebargetropicalcruises.com/
We haven't gone yet but Mote Acquarium is also in Sarasota -
http://mote.org/aquarium
I'm not much of a beach person but Siesta Key in Sarasota is supposed to be a really nice beach.