Now, as for the "other" things to do or see, you'll find out that if you come from the UK, Miami Beach looks more laike a small village than a City. But definitely visit Lincoln Road and Ocean Drive. Skip the Bass Museum of Art (nothing interesting there for Europeans), but find some time for the Smithmisterian Museum and the Erotic Art Museum.
Rent a jet ski on a bay side location and take a ride around Biscayne Bay (the ocean side is fine too, but the bay is more interesting, from the water).
Shop at Bayside (if you like fun places), Bal Harbour (if you're loaded) or Aventura (if you like the standard gigantic sized American shopping mall).
If being watched naked is not a strict necessity and you can dig a regular, not so crowded tropical beach with palm trees, head to Key Biscayne's Crandon Park.
If you want to see a surreal place (and you have a car), try to sneak into the old Hialeah Park. It's a closed down grandiose old-style hyppodrome in a not so great area of town (so you'll get to see the ugly Miami too...), with hundreds of free roaming flamingoes. BTW, it's a great place to bring a bull and have a thrill.....