If you are keen on gym leader rematches, then you will hear this very often. ;)
In Saffron city, concretely Silph Co., you can get a Hoenn starter from Steven Stone (yes, the Hoenn champion in the games Ruby and Sapphire, but not Emerald). He also feels like trading some Pokémon with you. I don't remember which Pokémon it is. Gotta check it out later. Also, in this building you can get a rare object to evolve Porygon to Porygon 2. Or was it Porygon 2 to Porygon Z? I can't remember.
In Viridian City you can battle some good trainers at Trainer's House, a big house west of the gym. You can also see the coffee gramps, the old man that gives you a TM; and the Pokémon Gym, which is lead by Gary Oak, although his name in the games is Blue.
In Pewter City you can fight Gym Leader Brock, visit the museum and receive an object that will allow you to encounter either Lugia or Ho-oh, depending on your version of the game. This is determined by which Pokémon you fight first in your game. For example, if you have Heart Gold, you have encountered Ho-oh, so you will get a Silver Wing or something like that. And viceversa.
Enjoy! =D
