Out on the beaches is perfectly safe, just don’t get run over. Idiots think that they can cross ,usually drunk ,where and whenever they want on the main road that is usually 40+ mph and four lanes in most places.
Downtown is safe now and really always has been,there’s lots of new developments and businesses . If you like art at all there is the Dali and the Saint Petersburg museum has a surprisingly impressive collection for a museum it’s size. The Don Cesar is a pretty unique old world style hotel if you make it down to that part of Saint Pete Beach.
Don’t go to the south side of St Pete at night, it’s the only real dangerous area, but it’s worst at night. Basically East of 49th Street and south of 5th Ave south, and east of I-275 south of downtown after 10 or so blocks. Some parts are gentrified but others are really not and it’s best not to find out which is which if you don’t have to.