Using the Cut ability, chop your way through to Route #9 from Cerulean City. Check into the Pokémon Center near the entrance to the Rock Tunnel, then plunge into the underground passage. It emerges on Route #10, a very short route to your next destination, Lavender Town. This might seem like a roundabout way to get there — but it's the only way.
1
Jr. Trainer♀
360
Oddish
LV18
Bellsprout
LV18
Oddish
LV18
Bellsprout
LV18
2
Hiker
700
Machop
LV20
Onix
LV20
3
Jr. Trainer♂
420
Growlithe
LV21
Charmander
LV21
Sandshrew
LV24
4
Bug Catcher
190
Beedrill
LV19
Beedrill
LV19
A
TM 30
5
Bug Catcher
200
Caterpie
LV20
Weedle
LV20
Venonat
LV20
6
Jr. Trainer♂
380
Rattata
LV19
Diglett
LV19
Ekans
LV19
Sandshrew
LV19
7
Hiker
735
Geodude
LV21
Onix
LV21
8
Hiker
700
Geodude
LV20
Machop
LV20
Geodude
LV20
9
Jr. Trainer♀
460
Meowth
LV23
Route #9 encounters
Spearow
35%
35%
20%
Fearow
N/A
N/A
4%
Rattata
40%
40%
20%
Raticate
N/A
N/A
8%
Ekans
25%
N/A
N/A
Sandshrew
N/A
25%
N/A
Nidoran♂
N/A
N/A
16%
Nidorino
N/A
N/A
8%
Nidoran♀
N/A
N/A
16%
Nidorina
N/A
N/A
8%
Route #10 encounters
Spearow
30%
30%
N/A
Sandshrew
N/A
30%
N/A
Rattata
15%
15%
20%
Raticate
N/A
N/A
10%
Ekans
30%
N/A
N/A
Nidoran♂
N/A
N/A
12%
Nidoran♀
N/A
N/A
12%
Machop
N/A
N/A
18%
Magnemite
N/A
N/A
28%
Voltorb
25%
25%
N/A
Before the tunnel
The encounters here are annoying, but at least many of them can be avoided and there's a Poké Center at the end. Make sure you have your Cut-knowing Pokémon with you, or the HM and a Pokémon who's willing to learn.
Before you enter the tunnel, hack aside the top bush and search beneath it for a Super Potion.
#100 Voltorb
#81 Magnemite
Voltorb appear entirely like Poké Balls. Despite being Electric type Pokémon, they learn no Electric attacks naturally without the aid of TMs. Rather, they learn Normal attacks including the life sacrificing Selfdestruct. Once learned, this move should only be used in an emergency.
The Magnemites in Yellow aren't as fast as their Voltorb cousins in Red/Blue, but their mix of strong Electric skills and Normal attacks are more versatile than the Normal-only skills of Voltorbs.
Power Plant
The Power Plant is visible from Route #10, but you can't reach it just yet. Sometime later, you'll obtain a Hidden Machine that will enable you to use the Surf technique. You'll be able then to travel along the stream that flows past both Route #10 and the Power Plant. Until then, you'll just have to keep your curiosity in check.