You can avoid the first trainer but not the second.
Misty's gym is a straightforward path around a pool. Defeat Brock to earn the Boulder Badge, which lets you use Flash outside of battle, and TM39, Rock Tomb. This gym specialises in Rock-type Pokémon, and Brock will use the attack Rock Tomb to seriously wound Pokemon like Charmander, Beedrill, and Pidgeotto. It doesn't have much of a puzzle but there is a lone trainer who you must face before taking on Brock, the leader. The first gym is located in Pewter City and is a Rock-type Gym.
Once you have all eight gym badges (proof of your victory against the Leader), you can take on Victory Road to go meet the Elite Four. Each gym focuses on a specific Pokemon type, giving you something to work with as you prepare your team for each challenge. These gyms, as with all Pokemon games, are spread out over the Kanto region. Pokemon FireRed and LeafGreen features the classic lineup of Gym Leaders from Red and Blue.
