Perhaps try some weekenders first. As I mentioned, DeSoto Pt is only a few (maybe 10) n.mi. from Gulfport. It’s a nice anchorage where you can go ashore, walk the beach of the Manatee River plus visit the DeSoto museum & see a film (at least you once could).
Also, you can anchor on the east (or west) side of Egmont Key. In winter boaters safely pick the east side when there is wind (or weather) from the west. Normally, you would not wish to be there in easterly wind of more a few knots, perhaps up to 8 or 10. Go ashore Egmont Key and walk the nice beach; also visit the “ruins.”
If you wish real seclusion and perhaps more adventure, there’s the anchorage at Terra Ceia, which is also an aquatic preserve. It’s “fun” getting in and out of there, however.
Another fun weekender from your location would be to anchor at Moore’s off the ICW, which is near Longboat Pass. Depending on weather, come down the outside and enter the ICW via Longboat Pass. Moore’s is south one or two n.mi. Go home up the ICW and exit the ICW at “The Bulkhead.” From there you choose your route home depending on your conditions, etc. NW across the Egmont Channel (must watch depth closely crossing the north side-check for updates), or NE to the south extension of the Maximo Channel, AKA the Sunshine Skyway Channel more properly, that runs along the approach to skyway bridge on its north side.
