Azalea Town and Ilex Forest
Cross Union Cave, stop Team Rocket, and earn the Hive Badge.
Slowpoke Well to Goldenrod
Bugsy, the second rival fight, and HM01 Cut
Travel south through Route 32 and Union Cave. In Azalea Town, speak to Kurt, then clear Team Rocket from Slowpoke Well. Bugsy's Lv.16 Scyther is the real threat: its Fury Cutter grows stronger on consecutive hits, so break the chain quickly with Fire, Flying, or Rock damage.
Heal before leaving town. Your rival waits at the west exit with Gastly, Zubat, and his evolved starter. After the battle, recover the Farfetch'd in Ilex Forest without stepping on branches behind it. Its owner gives you HM01 Cut, opening the route to Goldenrod City.