Violet City. Just right next door from Cherrygrove.

[Okay maybe they're not right next door to each other but this is the one exception where he will spare Shaun the details. Seriously, a whole week of hiking? You gotta be fuckin' kiddin' me...]

All you have to do is follow the trail. Don't wander anywhere else. It'll be a lot easier for you if you can find a buddy to go with. Is there anyone else nearby?