No problem
I've done this loads of times - most recently February in Florida - both as a student and now as a PPL. I have never been asked for ID or money up front. Everyone has been very friendly and helpful. The instructor can act as a guide and handle the radio so you can enjoy the flying. Why not pick a type to fly that you haven't tried before, or one with a glass cockpit?
I often ask if anyone else I'm with wants to fly and then book a 4 seater. I've flown to Sedona for breakfast, around Mount St Helen, from Boston up the coast to Maine, Florida loads of times.
I normally only book a few of days ahead, once I know what weather is likely. Just say you have a license but not FAA so need an instructor.
I've always logged the time as P/UT.