This is a great museum!
This museum is within walking distance to the Vinoy hotel, the Pier and many shops and restaurants. It has a diverse collection with a little of everything ranging from ancient history, Renaissance, African and Asian Art, modern art and everything else you can think of. There is a great website if you want more info. They have really good temporary shows, like Monet and Chihuly (both recently). If you aren't a real art lover you can view the entire collection in a couple of hours. If you are more interested (as I am) I would allow a half day to see it all. There are docent tours and some are fantastic, some so-so.
I would definitely recommend this museum (I like it better than the Dali and Tampa museum) and would plan on going during the daily mid-afternoon rain showers that are a part of daily life in St. Pete. It is well worth the money and would be fun for someone traveling aloneas well as a family. They truly have an impressive collection.