Not all that much to do here. You can go right to the Gym if you want to, but you should probably heal at the Pokemon Center first and possibly restock your supplies in the Poke Mart if you burned through any.
A lady in the first house from the Ice Path will trade you a Dodrio for your female Dragonair. She won't take a male one, just a female one. But you know what? That's a bad trade, because Dragonairs are a pain to get and Dodrios are comparatively common. Don't waste your time.
The house on the west side of town has a bunch of people in it that may be of use to you. Inside, you can find:
- The Move Deleter (balding person on the left), who will delete your Pokemon's moves (including HM moves! Bye-bye Cut!)
- The Move Maniac (the guy next to the Move Deleter), who will teach your Pokemon any move it could have learned by leveling up (up to its current level) if you give him a Heart Scale (which can be found by using Rock Smash on rocks)
- Grandma Wilma (the old lady at the table), who will teach Draco Meteor to your Dragon-type Pokemon if it has max happiness
- and the Ultimate Move Tutor (Elemental Hyper Beams) (the old man at the table), who will teach Blast Burn to your Typhlosion, Frenzy Plant to your Meganium, or Hydro Cannon to your Feraligatr. (He'll also teach this move to top-stage starters from other regions, like Charizard, Swampert, etc.).
You can also get your Effort Ribbon by talking to a lady inside of one of the houses. She'll give it to your lead Pokemon, but only if it has received maximum Effort Values. Basically, if your Pokemon has done lots of fighting and Vitamins will no longer affect it, ever, then it will get that Ribbon.
That's pretty much it. There's the Dragon's Den behind the Gym on the northern side of town, but you won't be able to enter it just yet. When you're done, make your way into the Gym!