Hi Ted,
My in-laws are in St. Pete and I have practiced at Mangrove Bay Golf Course. It's a city-operated course, but I think the practice facilities will be fine for what you need. They have grass tees, and also separate pitching / sand practice greens.
I believe Brittany Lincicome used to play there, so that may be an indirect testimonial to its practice capabilities. It's also a First Tee location, and those tend to have above-average practice facilities.