The first one in Johto- the region I'm assuming you're in, if you didn't take the ferry in New Bark Town, is in Violet City- it's just after Cherrygrove, and it shouldn't be more than a couple day's travel. Violet's gym is Flying Type.

( she'd put it off more than she truly wanted to because early on she wound up with an abundance of grass or bug types... and yes she trained them well, but she had no desire to do that to them. jasper wound up being the exception, if only because he was also electric type. )

For what it's worth, there isn't any mandatory order to do them in, but the cities are pretty linear for the most part.