After you pull the plug on Lt. Surge, head for Lavender Town. The quickest way is to the Route #11 and #12. Unfortunately, a Snorlax blocks Route #12, but you should go as far as the lookout station. There you'll meet up with one of Professor Oak's aides. After you've talked with him, turn around and head toward Diglett's Cave.
Drowzees are incredible. They have lots of HP and good special attacks, including a variety of Psychic attacks that do damage and give your opponents negative conditions. But the best thing about Drowzee is that he can learn Dream Eater from TM 42 (which you'll get very shortly when you return to Viridian City), and that combined with his built-in skill Hypnosis, is one of the game's most powerful combos. He puts them to sleep with Hypnosis then uses Dream Eater to deal a ton of damage and gain it all back as health.
This area is entirely optional, since you'll need to use Diglett's Cave to cross back to Route 2 (where you want to be right now) without facing the wrath of the 10 deranged trainers lurking in Route #11. But you might want to visit for a bit to get yourself a Drowzee, and maybe take down some of the Gamblers for the massive amounts of cash they keep on hand. NOTE: Checking the lone bush that a Youngster (marked on the map as Trainer No. 8) is facing will yield an Escape Rope.
The checkpoint to the East is open, but a sleeping Snorlax is blocking the path. You can go upstairs, however, and get the Item Finder from one of Professor Oak's aides if you have 30 or more Pokémon, or trade Nidorino for a Nidorina in Red/Blue or a Lickitung for a Dugtrio in Yellow.
Drowzee
Ekans
Pidgeotto
Raticate
1260