You've liberated Saffron City from Team Rocket's mad scheme, and you could probably use a bit of a holiday. We hear the fishing is good down south of Lavender Town, so grab your Old Rod and get set to drown a few worms. You ought to pack the Poké Flute, too. You won't be able to avoid Pokémon duels completely on this trip, but things will be far less hectic. Route 13 is more like a maze than a highway, but it is a pleasant place to walk and enjoy the great outdoors.
Sleeping Beauty
You'll need to use your Poké Flute to wake the Snorlax blocking the path here, but stop at that first building and get TM 39 first. It contains Swift, a good attack that virtually always hits (even if they're using Dig or Fly). The Poké Flute has the power to wake a sleeping Pokémon, in or out of battle. Pipe a sweet tune to rouse this Snorlax from its rather inconvenient resting place. It won't be very happy about the wake-up call and when it attacks, you can try to capture it. This is the only other Snorlax in the game, so if you didn't catch the one in Route #16, here's another opportunity. With the way clear, you can continue south to Route 13, but first head a bit west of where the Snorlax once rested and examine the bottom-right tree jutting onto the path: you'll find a Hyper Potion. After that, get the Super Rod in the second building on the route.
Moving on
If you want that Farfetch'd (finally, a Farfetch'd that isn't named Dux, but it's only in Yellow), or the Iron, you'll need to get a Cut-equipped Pokémon to hack your way through the tree. Fortunately, TM 16 (the Pay Day skill) and the hidden PP Up (to the left of Trainer A on Route #13) are easier to get. There's also a hidden Calcium on the other side of Trainer A -- both items can be found on spots where the southern fence is missing. Save that PP Up for one of the power skills: Thunder, Blizzard or Fire Blast. Yellow players can also get a chance at a Slowpoke here just by using Surf and walking the waves of Route #12.
1
Fisherman
770
Goldeen
LV22
Poliwag
LV22
Goldeen
LV22
2
Fisherman
840
Tentacool
LV24
Goldeen
LV24
3
Fisherman
945
Goldeen
LV27
4
Fisherman
735
Poliwag
LV21
Shellder
LV21
Goldeen
LV21
Horsea
LV21
5
Rocker
725
Voltorb
LV29
Electrode
LV29
6
Fisherman
840
Magikarp
LV24
Magikarp
LV24
7
Jr. Trainer
840
Nidoran♂
LV29
Nidorino
LV29
A
TM 16
B
Iron
Route #12 encounters
Pidgey
35%
35%
15%
Pidgeotto
N/A
N/A
10%
Venonat
20%
20%
N/A
Bellsprout
N/A
40%
25%
Weepinbell
N/A
5%
5%
Farfetch'd
N/A
N/A
5%
Oddish
40%
N/A
35%
Gloom
5%
N/A
5%
Slowpoke
N/A
N/A
95%
Slowbro
N/A
N/A
5%
Route #12 Fishing (Super Rod)
Magikarp
25%
25%
N/A
Goldeen
25%
25%
N/A
Horsea
N/A
N/A
70%
Seadra
N/A
N/A
30%
Tentacool
25%
25%
N/A
Krabby
25%
25%
N/A
8
Birdkeeper
625
Spearow
LV25
Pidgey
LV25
Pidgey
LV25
Spearow
LV25
Spearow
LV25
9
Biker
700
Koffing
LV28
Koffing
LV28
Koffing
LV28
A
Birdkeeper
650
Pidgey
LV26
Pidgeotto
LV26
Spearow
LV26
Fearow
LV26
B
Birdkeeper
650
Pidgey
LV26
Spearow
LV26
Pidgey
LV26
Fearow
LV26
C
Birdkeeper
700
Pidgey
LV28
Pidgeotto
LV28
Doduo
LV28
D
Birdkeeper
725
Pidgeotto
LV29
Fearow
LV29
E
Birdkeeper
700
Spearow
LV28
Doduo
LV28
Fearow
LV28
1
Jr. Trainer?
560
Goldeen
LV28
Poliwag
LV28
Horsea
LV28
2
Birdkeeper
725
Pidgey
LV29
Pidgeotto
LV29
3
Jr. Trainer?
480
Pidgey
LV24
Meowth
LV24
Rattata
LV24
Pikachu
LV24
Pidgey
LV24
Meowth
LV24
4
Beauty
1890
Rattata
LV27
Pikachu
LV27
Vulpix
LV27
Rattata
LV27
5
Beauty
2030
Clefairy
LV29
Meowth
LV29
6
Jr. Trainer?
600
Poliwag
LV30
Poliwag
LV30
7
Jr. Trainer?
540
Pidgey
LV27
Meowth
LV27
Pidgey
LV27
Pidgeotto
LV27
Route #13 encounters
Pidgey
30%
30%
10%
Pidgeotto
N/A
N/A
15%
Venonat
20%
20%
N/A
Bellsprout
N/A
40%
25%
Weepinbell
N/A
5%
5%
Farfetch'd
N/A
N/A
5%
Oddish
40%
N/A
35%
Gloom
5%
N/A
5%
Ditto
5%
5%
N/A
Slowpoke
N/A
N/A
95%
Slowbro
N/A
N/A
5%
Route #13 Fishing (Super Rod)
Magikarp
25%
25%
N/A
Goldeen
25%
25%
N/A
Horsea
N/A
N/A
70%
Seadra
N/A
N/A
10%
Tentacool
25%
25%
20%
Krabby
25%
25%
N/A
#118 Goldeen
#98 Krabby
Now that you have the Super Rod, you'll be able to fish for more Water-type Pokémon than you know what to do with. So you might wish to ignore the less-interesting ones like Goldeen. Evolved form Seaking is fairly tough, but with nothing but a handful of ordinary Normal attacks, she's not that intriguing.
Krabby is a fairly good Water Pokémon, and you can have fun beating things instantly (30% of the time) with his Guillotine technique. But Krabby's real selling point is that he can learn Cut, Surf and Strength HM's, allowing you to have them all without using more than one slot on your bench.
#116 Horsea
#72 Tentacool
Horsea's evolved form Seadra is a solid fighter, and learns a good variety of Water-type attacks. But you probably won't want more than one or two Water-types on your bench, and there's a variety of better options. Wartortle, Cloyster and Gyarados top the list.
Tentacool mixes Water with Poison-types, and learns a variety of good attacks in both (and has a high enough Special to make good use of them). Built-in Poison attack Acid does damage while lowering Defense, which is nice, but Poison-types still aren't stellar.