Pryce specializes in Ice pokémon. His Gym has slippery ice patches, so you will have to do some thinking, and possibly some trial and error, to figure out how to end up where you want to go. There are a few trainers here.
After you defeat Pryce, you will be able to use Waterfall outside of battle. This means you can go to Mt. Mortar and get a Tyrogue. Tyrogue is a baby fighting type pokémon that can evolve into three different things, depending on its stats when it evolves. The evolved forms all make Tyrogue eggs if they are bred, so you can try again until you have all three.
Nothing left to do in Mahogany Town now except go east (the guy will finally let you pass).