The Museum of Science is located on the north side of the city. Pay a few bucks to get in and see the exhibits. There’s really nothing of interest there other than some fossils, so you can skip it all together.
When you think your team is ready, head to the Pokemon Gym on the west side of town.
Pewter City Gym
The Pewter City Gym supposedly specializes in Rock-type Pokemon, but the first trainer will use only Ground-type Pokemon. If you chose Bulbasaur or Squirtle in Red or Blue, you will have an easy time going through. If you chose Charmander, things may be a bit difficult. The best option is to use Butterfree’s Confusion at Level 12 to deal the most damage.
When you come up against Brock, he might use the move Bide. This will allow Onix to take in damage for two turns and unleash it on the third with double the power. If you see Onix use bide, switch to status move like growl and leer to reduce his attack and defense. If you attack and don’t make him faint, there’s a good chance Onix will cause your Pokemon to faint at the end of Bide.
Once you defeat Brock you will earn the Boulder Badge, which boosts the attack stat of your Pokemon and allows you to use HM05 Flash outside of battle. You will also get TM34 – Bide. As mentioned earlier, Bide takes in damage for two turns and then attacks with twice the damage it received during those turns.
Now that you have the Boulder Badge, you can go east to Route 3.