I want to give my hints about Sarasota, as an ex-native. I went to high school in Sarasota and can help by giving some insider advice.
#1. Siesta Key Beach - must go there! Rated one of the world's 10 prettiest beaches many years ago by Time Mag and it still lives up to its reputation. Sand like baby powder, blue water, dolphins.
#2. The Ringling Museum - an extrordinary museum for such a small city. The collection is quite extensive and the museum is very well laid out.
#3. Longboat - way too expensive.
Myaka - more geared towards the nature end of the spectrum. Spanish Point - the lives of the settlers.
Time not to go - winter!! Beware: even though the weather is the best weather-wise, the traffic and lines quadruple. For example, on US41, it took me 15 minutes to drive from home to Osprey during the off-season. Took me about an hour during the on-season.