According to my recently posted condo rental market update for downtown St Petersburg the market is alive and well, with a 9 month inventory.
Annual rentals are available from $750/month for a small 1 bedroom or efficiency, up to $5,000/month for a luxury 3 bedroom unit. It's hard to find a seasonal rental in downtown St Pete, but there are lots of selections on the Gulf beaches, from St Pete Beach to Clearwater Beach. Most are annual rentals due to building restrictions, only a few are age restricted, and some allow pets. Most, but not all, have secured parking, generally under the building.
Between the condo buildings are shops and restaurants. Across Beach Drive are beautiful public parks and a museum, and beyond the park are yacht basins and a view of Tampa Bay. Downtown St Pete is very pedestrian friendly - you can go days without wanting to get in your car.