A few more suggestions:
Not in St Pete but across the bridge in Tampa is the iconic Berns Steak House. Expensive and often difficult to get reservations. Extraordinary experience. Be sure to read the background history either online or on the menu. One unique fact was that Bern was a vegetarian.
After dinner, they offer a tour of the kitchen and wine cellar.(May have been suspended). Use to be conducted by your waiter. Lately it's been more of a tour group affair.
Then go upstairs to a separate restaurant for dessert. Unique and house made desserts accompanied by cocktails, cordials, rare dessert wines and more.
On the other end of the spectrum, VIP lounge on Treasure Island.
A dive, hole in the wall, a favorite local hangout and popular with repeat visitors. They've opened additional restaurants but the tiny one on TI is the original. You might even see my little brother there sipping on a bourbon on the rocks and flirting with the bartender. Food is Tex-Mex and is pretty good.
The Hurricane on St Pete Beach. Food is so so but the view from the open air, rooftop lounge is worth the price of a drink or two.