Blackthorn City hasn't got much in it – you can buy Ultra Balls and Max Repels at the mart and there is a trainer who wants to do a really bad swap with you, either a Dodrio (Silver/Crystal) or a Rhydon (Gold) for a female Dragonair. Both Rhydon and Dodrio are rare and decent Pokémon, but Dragonair is one of the best Pokémon in the game, and will evolve into an even more powerful beast, Dragonite, at Level 55. Still, if you have a Dragonair, you probably bought a Dratini at the game corner (Gold) and raised it up – so you know already that giving it away would be a terrible idea.
There is also a move deleter, who can make your Pokémon forget HM moves. You may want to do this, but the main thing is getting that final badge. It is recommended that you bring your Red Gyarados and an Ice Pokémon (something like a Swinub or a Jynx) and go to the Gym.