Part 1: New Bark Town to Violet City — Falkner

The opening run: Routes 29 to 31, Cherrygrove, Dark Cave's south side, Sprout Tower and the Ruins of Alph.

New Bark Town to Violet City — Falkner opens 14 areas. There are 26 trainers standing in them. The fights at this checkpoint are Crystal, Gold, Falkner 1, and 3 more.

Where to go

1. Cherrygrove City

   Wild: Magikarp 70% · Lv 10, Basculin (Basculin Blue Striped) 60% · Lv 20, Shellder 60% · Lv 15-19, Qwilfish 40% · Lv 40 +4 more

   Trainers: Passerby (Chikorita) Lv 5, Passerby (Cyndaquil) Lv 5, Passerby (Totodile) Lv 5

   Pick up: TM20 Safeguard, Mystic Water (gift)

2. Dark Cave South Side

   Wild: Magikarp 94% · Lv 5-19, Barboach 60% · Lv 20, Lumineon 40% · Lv 40, Zubat 40% · Lv 3-6 +7 more

   Pick up: Dusk Stone (item ball)

3. New Bark Town

   Wild: Tentacool 90% · Lv 25-29, Magikarp 70% · Lv 10, Chinchou 40% · Lv 40, Finneon 40% · Lv 20 +3 more

   Trainers: ★ Crystal Lv 4, ★ Gold Lv 4

   Pick up: HM08 Dive

4. Route 29

   Wild: Pidgey 40% · Lv 2-3, Zigzagoon 20% · Lv 2-3, Rattata 16% · Lv 2-3, Hoppip 14% · Lv 2-3 +1 more

   Pick up: Silk Scarf (gift)

5. Route 30

   Wild: Poliwag 90% · Lv 15-24, Magikarp 70% · Lv 10, Poliwhirl 40% · Lv 40, Shellos 40% · Lv 40 +8 more

   Trainers: Bug Catcher Don Lv 4, Youngster Mikey Lv 4, Youngster Joey Lv 5

6. Route 31

   Wild: Poliwag 90% · Lv 15-24, Carvanha 70% · Lv 10, Poliwhirl 40% · Lv 40, Bellsprout 30% · Lv 4-5 +7 more

   Trainers: Bug Catcher Wade Lv 6, Cooltrainer Nate Lv 8

   Pick up: Air Balloon (gift)

7. Ruins of Alph B1F

   Wild: Unown 100% · Lv 5

8. Ruins of Alph Outside

   Wild: Geodude 90% · Lv 30, Carvanha 70% · Lv 10, Wooper 65% · Lv 25-33, Magikarp 44% · Lv 10-40 +14 more

   Trainers: Psychic Nathan Lv 41, Super Nerd Stan Lv 41

   Pick up: TM96 Nature Power

9. Sprout Tower 2F

   Wild: Rattata 40% · Lv 3-6, Gastly 20% · Lv 3-6, Yamask 20% · Lv 3-6, Duskull 9% · Lv 3-7 +2 more

   Trainers: Sage Nico Lv 5, Sage Edmond Lv 7

10. Sprout Tower 3F

    Wild: Rattata 40% · Lv 3-6, Gastly 20% · Lv 3-6, Yamask 20% · Lv 3-6, Duskull 9% · Lv 3-7 +2 more

    Trainers: Sage Neal Lv 8, Sage Troy Lv 8, Sage Jin Lv 9, Elder Elder Li Lv 10, Elder Elder Li (8 Badges) Lv 61

    Pick up: HM05 Flash

11. Violet City

    Wild: Magikarp 70% · Lv 10, Poliwag 65% · Lv 15-24, Horsea 40% · Lv 40, Shellos 30% · Lv 15-24 +3 more

    Pick up: TM19 Roost, TM76 Hone Claws

12. Sprout Tower 1F

    Trainers: Sage Chow Lv 6

13. Violet City Gym

    Trainers: Bird Keeper Rod Lv 10, Bird Keeper Abe Lv 11, ★ Falkner 1 Lv 12, ★ Falkner 1 (Hard) Lv 13

14. Violet City Trainer School

    Trainers: ★ Falkner (Postgame Rematch) Lv 76, ★ Falkner (Postgame Rematch, Hard) Lv 78

★ Crystal — New Bark Town

1 Pokémon · level cap Lv 4 (every cap) · Crystal’s own page

	Pokémon	Moves
	Marill Lv 4 · Thick Fat Innates: Cheek Pouch, Water Veil	Pound Tail Whip

★ Gold — New Bark Town

1 Pokémon · level cap Lv 4 (every cap) · Gold’s own page

	Pokémon	Moves
	Marill Lv 4 · Thick Fat Innates: Cheek Pouch, Water Veil	Pound Tail Whip

★ Falkner 1 — Violet City Gym

3 Pokémon · level cap Lv 12 (every cap) · Falkner 1’s own page

	Pokémon	Moves
	Pidgey Lv 11 Innates: Run Away	Tackle Gust Quick Attack
	Gligar Lv 11 Innates: Poison Touch	Quick Attack Poison Sting Harden
	Pidgeotto Lv 12 · Oran Berry Innates: Vital Spirit, Windburst	Tackle Mud Slap Peck

Also fought around here

Everything you can have caught by this checkpoint · Open the interactive guide

It also doesn't say when Dark Cave North Side opens up, so it is in no part above; it has its own route page.