I used to live there and still live within an hours drive. In the downtown area this is a shopping and entertainment complex called BayWalk. It has several restaurants and a movie theater and some eclectic shops and upscale clothing stores. The Dali museum is near there, as are several others including a Holocaust museum. There is a pier large enough to drive on that extends into Tampa Bay that is always a favorite with tourists, it has shops and restaurants at the end.
You did not mention if you were referring to the beach part of St Petersburg. If you are going to the beach area there are alot of beaches that all run together. There is an area called John's Pass Village at Maderia Beach that many enjoy, it has lots of shops. If you are looking for incredible food out near the beaches is you go north to Indian Rocks Beach there is a well known restaurant called Salt Rock Grill. Expensive but worth it.
Let me know if you have any more questions.