Like Route 2 before it, Route 4 is split into two sections, separated by Mt. Moon in this case. This part of Route 4 has very little to offer, since there are no patches of grass on this side, but there is a Pokémon Center over here as well as a Coach Trainer near the entrance of the route.
Talk to the Coach Trainer and take him on in a battle.
You may not want to finish this fight so quickly. Oberon’s Meowth uses Pay Day, which scatters coins on the battlefield that are picked up after the fight is over. If you have a little patience, you can just switch around your Pokémon so Meowth can use Pay Day over and over against you. Extra points if you’re able to lower its Attack with something like Growl so it will be able to hit you with Pay Day more often.
After you’re victorious, you’ll be rewarded with TM57 Pay Day, the very move that Meowth used against you. Since the only renewable way for you to gain EXP is by catching Pokémon and since you can’t rematch most Trainers, you may end up running low on Poké Balls or funds to buy other items with. Having a Pokémon use Pay Day will help net you some extra funds — each use of Pay Day results in 5 times the user’s level, so a Pokémon at level 10 using Pay Day will drop 50 each time the move is used, and you can use it multiple times per battle. Think carefully whether that’s important to you or not, since it has just 40 base power. On the bright side, at least both Pikachu and Eevee can learn the move, although they’re going to be getting much better moves later on.
There’s an Escape Rope you can pick up just to the left of the Pokémon Center. You’re about to enter Mt. Moon, and since it’s a pretty large cave, that can be helpful to quickly return to the entrance.
Inside of the Pokémon Center are a few things of interest. One of which is the Jigglypuff on the right side of the room, which will put your partner Pokémon to sleep in a cutscene if you shake the Joy-Con or Poké Ball Plus after talking to it. (Don’t worry, it doesn’t actually gain the “asleep” status.)
There’s also a guy in the top-left part of the Pokémon Center that will sell you a level 5 Magikarp for “just” 500. Magikarp is a pretty worthless Pokémon, but it’s also one that you don’t yet have access to just yet, so picking one up now and leaving it in your party until it evolves into the fearsome Gyarados at level 20 might not be a bad idea. It’s not going to do you any good until then, but you’re unlikely to need a full team of usable Pokémon since your partner Pikachu or Eevee are strong enough at this point, so it will save you time later on.
Whenever you’re ready, head on into Mt. Moon to the east of the Pokémon Center.