There are public buses runing from SRQ to Anna Maria Island, Longboat Key, and Lido, for sure,and probably to Siesta a well. Be aware it would involve at least one transfer, probably more, and with luggage would be difficult at best.
A taxi to Siesta or south Longboat would be around $30-35, Anna Maria is farther. That would be your best bet. Wihout a car on island, Anna Maria would be easiest, because of the free trolley. Longboat is spread out and from any given point is not likely to be walkable to anything. If you are going to Siesta stay near the village for walkable.Edited: 30 November 2012, 19:53
Kris makes good points (as usual!). Since you don't want to rent a car, a taxi is your next best option. The public bus service -- called MCAT for Anna Maria and SCAT for Longboat, Lido and Siesta -- all would require at least one transfer; with somewhat infrequent schedules, it would probably take you between 1 to 2 hours from the airport to your destination, compared with 30 minutes or less in a car.
You could always call a local shuttle service but the taxis that wait at the airport are normally the same or at a lower cost.
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