Part 4: Got HM01 Cut — S.S. Anne
Cut (HM01) is given on the S.S. Anne. The sailor in Vermilion City checks for the S.S. Ticket, which Bill hands over at his sea cottage on Route 25, and Cut only works outside battle once you have Misty's badge. It opens Route 9 out of Cerulean, the Route 2 end of Diglett's Cave, and the Vermilion Gym door.
Got HM01 Cut — S.S. Anne opens 10 areas. There are 87 trainers standing in them. The fights at this checkpoint are Rival Blue (Bulbasaur), Rival Blue (Charmander), Rival Blue (Squirtle), and 1 more.
Where to go
Rock Tunnel
Wild: Geodude 95% · Lv 5-30, Zubat 30% · Lv 15-16, Machop 15% · Lv 16-17, Mankey 15% · Lv 16-17 +2 more
Trainers: Hiker Allen Lv 25, Hiker Dudley Lv 21, Hiker Eric Lv 20, Hiker Lenny Lv 19, Hiker Lucas Lv 21, Hiker Oliver Lv 20 +9 more
Pokémon Tower
Wild: Gastly 90% · Lv 13-19, Haunter 15% · Lv 23-25, Cubone 10% · Lv 17-19
Trainers: ★ Rival Blue (Bulbasaur) Lv 25, ★ Rival Blue (Charmander) Lv 25, ★ Rival Blue (Squirtle) Lv 25, Channeler Angelica Lv 22, Channeler Carly Lv 24, Channeler Emilia Lv 24 +13 more
Route 7
Wild: Meowth 40% · Lv 17-20, Pidgey 30% · Lv 19-22, Bellsprout 20% · Lv 19-22, Oddish 20% · Lv 19-22 +2 more
Route 8
Wild: Meowth 30% · Lv 18-20, Pidgey 30% · Lv 18-20, Ekans 20% · Lv 17-19, Growlithe 20% · Lv 15-18 +2 more
Trainers: Biker Jaren Lv 24, Biker Ricardo Lv 23, Gamer Rich Lv 24, Gamer Stan Lv 22, Lass Andrea Lv 24, Lass Julia Lv 22 +6 more
Route 9
Wild: Rattata 40% · Lv 14-17, Spearow 35% · Lv 13-17, Ekans 25% · Lv 11-17, Sandshrew 25% · Lv 11-17
Trainers: Bug Catcher Brent Lv 19, Bug Catcher Conner Lv 20, Camper Chris Lv 21, Camper Drew Lv 19, Hiker Alan Lv 21, Hiker Brice Lv 20 +3 more
Pick up: TM40 Aerial Ace
Route 10
Wild: Magikarp 100% · Lv 5, Tentacool 100% · Lv 5-40, Horsea 84% · Lv 15-35, Krabby 84% · Lv 15-35 +7 more
Trainers: Hiker Clark Lv 21, Hiker Trent Lv 19, Picnicker Carol Lv 21, Picnicker Heidi Lv 20, Pokémaniac Herman Lv 20, Pokémaniac Mark Lv 29
Route 12
Wild: Magikarp 100% · Lv 5, Tentacool 100% · Lv 5-40, Horsea 84% · Lv 15-35, Krabby 84% · Lv 15-35 +10 more
Trainers: Camper Justin Lv 29, Fisherman Andrew Lv 24, Fisherman Chip Lv 24, Fisherman Elliot Lv 21, Fisherman Hank Lv 27, Fisherman Ned Lv 22 +2 more
Pick up: TM27 Return, TM48 Skill Swap
Celadon City
Wild: Magikarp 100% · Lv 5, Psyduck 99% · Lv 5-40, Slowpoke 99% · Lv 5-40, Grimer 1% · Lv 30-40 +4 more
Trainers: Team Rocket Grunt Lv 20
Pick up: TM19 Giga Drain
Saffron City
Wild: Hitmonchan Lv 25, Hitmonlee Lv 25, Lapras Lv 25
Trainers: Black Belt Aaron Lv 36, Black Belt Hideki Lv 32, Black Belt Hitoshi Lv 31, Black Belt Koichi Lv 37, Black Belt Mike Lv 31
Pick up: TM04 Calm Mind, TM29 Psychic
Rocket Hideout
Trainers: ★ Boss Giovanni Lv 29, Team Rocket Grunt Lv 21, Team Rocket Grunt Lv 21, Team Rocket Grunt Lv 20, Team Rocket Grunt Lv 19, Team Rocket Grunt Lv 22 +6 more
★ Rival Blue (Bulbasaur) — Pokémon Tower
| Pokémon | Ability & item | Moves | Base stats | |
|---|---|---|---|---|
 | Pidgeotto Lv 25 NormalFlying | Sand Attack Gust Quick Attack Whirlwind | HP63Attack60Defense55Sp. Atk50Sp. Def50Speed71Total349 | |
 | Gyarados Lv 23 WaterFlying | Ability Intimidate | Thrash Bite | HP95Attack125Defense79Sp. Atk60Sp. Def100Speed81Total540 |
 | Growlithe Lv 22 Fire | Roar Ember Leer Odor Sleuth | HP55Attack70Defense45Sp. Atk70Sp. Def50Speed60Total350 | |
 | Kadabra Lv 20 Psychic | Teleport Kinesis Confusion Disable | HP40Attack35Defense30Sp. Atk120Sp. Def70Speed105Total400 | |
 | Ivysaur Lv 25 GrassPoison | Ability Overgrow | Vine Whip Poison Powder Sleep Powder Razor Leaf | HP60Attack62Defense63Sp. Atk80Sp. Def80Speed60Total405 |
★ Rival Blue (Charmander) — Pokémon Tower
| Pokémon | Ability & item | Moves | Base stats | |
|---|---|---|---|---|
| Pidgeotto Lv 25 NormalFlying | Sand Attack Gust Quick Attack Whirlwind | HP63Attack60Defense55Sp. Atk50Sp. Def50Speed71Total349 | |
 | Exeggcute Lv 23 GrassPsychic | Ability Chlorophyll | Hypnosis Reflect Leech Seed Confusion | HP60Attack40Defense80Sp. Atk60Sp. Def45Speed40Total325 |
| Gyarados Lv 22 WaterFlying | Ability Intimidate | Thrash Bite | HP95Attack125Defense79Sp. Atk60Sp. Def100Speed81Total540 |
| Kadabra Lv 20 Psychic | Teleport Kinesis Confusion Disable | HP40Attack35Defense30Sp. Atk120Sp. Def70Speed105Total400 | |
 | Charmeleon Lv 25 Fire | Ability Blaze | Growl Ember Metal Claw Smokescreen | HP58Attack64Defense58Sp. Atk80Sp. Def65Speed80Total405 |
★ Rival Blue (Squirtle) — Pokémon Tower
| Pokémon | Ability & item | Moves | Base stats | |
|---|---|---|---|---|
| Pidgeotto Lv 25 NormalFlying | Sand Attack Gust Quick Attack Whirlwind | HP63Attack60Defense55Sp. Atk50Sp. Def50Speed71Total349 | |
| Growlithe Lv 23 Fire | Roar Ember Leer Odor Sleuth | HP55Attack70Defense45Sp. Atk70Sp. Def50Speed60Total350 | |
| Exeggcute Lv 22 GrassPsychic | Ability Chlorophyll | Hypnosis Reflect Leech Seed Confusion | HP60Attack40Defense80Sp. Atk60Sp. Def45Speed40Total325 |
| Kadabra Lv 20 Psychic | Teleport Kinesis Confusion Disable | HP40Attack35Defense30Sp. Atk120Sp. Def70Speed105Total400 | |
 | Wartortle Lv 25 Water | Ability Torrent | Withdraw Water Gun Bite Rapid Spin | HP59Attack63Defense80Sp. Atk65Sp. Def80Speed58Total405 |
Also fought around here
It also doesn't say when 4 of its areas open up, so they are listed together in the last part rather than guessed into the story.