Since you don't have any Pokémon with Cut (yet), you'll have to go through the grass on the right. In front of you is the entrance to the Dark Cave; you won't be able to see a thing in there until you get Flash, but you can wander back and forth just inside the entrance until a random encounter offers you a wild Geodude - he'll be very useful in the Violet City Gym battle you're coming up on. Don't forget to collect the Potion next to the Cave, and the Bitter Berry on the tree next to the sleeping man (remember him, he'll be important later). Turn south and battle Bug Catcher Wade, then collect the loose Poké Ball. Turn west through the grass, up the hill and through the gatehouse into Violet City.
Caterpie
Pidgey
Zubat
Bellsprout
Hoothoot
Weedle
Hoppip