GTA Vice City had a great way of sealing off the western half of the map at the earlier stages; the storms were a believable method of limiting the game. It's a minor thing, but I definately liked that.
Favorites:
Engine noises which matched the vehicles (I could be wrong, but I thought GTA:VC was the first to do this outside of racing sims).
Cash, not Kudos.
The name of the Vespa.
Delivering pizzas.
Landing a helicopter in Little Haiti and being car-jacked right out of it.
Creating disturbances at the Golf Course.
Lance Vance.
Listening to the conversations of NPCs. "I never asked your sister out!"
Ammu-Nation.
Backing up the car-carriers into pedestrians, so they'd wind up walking right up the back of the truck.
Radio Espantoso.
Vrock. For people who wear nametags to work.
They also had another station bump which was great, but I forget the wording. It was something like, "while the other stations are at school, we're out shoplifting"
The world of the original Vice City was fantastic. I loved everything about it, especially the inclusion of motorcycles. The whole 80's vibe was great and I'd love to re-visit that (with new elements added) thanks to CheapyD, Wombat, and Rockstar!
Because GTA never dissapoints. There's always something to do if you're having a tough time with a missiion, and you don't have to do the missions in order most of the time.
Albiet a little on the flat side in contrast to GTA: III, Vice City certainly put out in a literal sense. It made me go into heat soon afterwards. I love it.