Tough question because it depends on everyone's taste. First- there's nothing to see in Palm Beach Gardens. It's nice, don't get me wrong, but it's nothing more than a great northern suburb in Palm Beach County. If you want to go shopping you'll love PBG. The best I can recommend in PBG are the beaches and the beautiful homes on Ocean Drive. You'll find them as you drive up and down the beach. Miami has lots more to offer. In Miami, you can take a boat tour of Star Island, see 1920's era Old Miami (also along Ocean Drive- just in Miami, now) or see the World Erotic Art Museum...again it depends on taste. But FYI- it's a pretty interesting museum and not full of porn. Personally, I would skip Palm Beach Gardens, if possible and head to Fort Lauderdale. The Las Olas area has a great club/bar/lounge/artsy mix in the evenings. about 8 years ago
Miami I would recommend Viscaya mansion tour, and any of the catamaran tours of the Islands. Ocean Drive at night for people watching and too many clubs to give only one whe. It comes to South Beach. Go to Versace's semi-private restaurant/club as it is one of a kind.
Palm Beach Gardens I would recommend outdoors activities such as MacArthur State Park, also tour Palm Beach via the bike tour, Flager Museum on Palm Beach, have drinks and dinner at the Breakers on Palm Beach. If you have any golfers the you won't find more golf courses in the world then in Palm Beach County. Shopping is good at the Gardens Mall or of course Worth Ave in Palm Beach. Any boating (rent a large one for everyone) is great, especially up and down the intracoastal. Drive by Tiger Woods and Celine Dion's new houses on Jupiter Island. Clematis Street in West Palm Beach on Thursday nights is a blast. about 8 years ago