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.
Route #11 encounters
Spearow
35%
35%
N/A
Ekans
35%
N/A
N/A
Sandshrew
N/A
35%
N/A
Drowzee
30%
30%
25%
Pidgey
N/A
N/A
35%
Pidgeotto
N/A
N/A
5%
Rattata
N/A
N/A
30%
Raticate
N/A
N/A
5%
1
Gambler
1260
Poliwag
LV18
Horsea
LV18
2
Youngster
315
Ekans
LV21
3
Youngster
285
Sandshrew
LV19
Zubat
LV19
4
Youngster
270
Nidoran♂
LV18
Nidoran♀
LV18
5
Gambler
1260
Bellsprout
LV18
Oddish
LV18
6
Gambler
1260
Growlithe
LV18
Vulpix
LV18
7
Engineer
1050
Magnemite
LV21
8
Youngster
255
Rattata
LV17
Rattata
LV17
Raticate
LV17
9
Gambler
1260
Voltorb
LV18
Magnemite
LV18
A
Engineer
900
Magnemite
LV18
Magnemite
LV18
Magneton
LV18
A Snorlax in the way
#96 Drowzee
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.