Uh, there are a few, but they are really small. The Flagstaff Athletic Center is pretty nice and they have a huuuuge East Flagstaff center and a smaller West Flagstaff location. If you watch the paper, they should be running a deal now where they are waiving sign-up fees or slashing them as their anniversary promotion. After the sign-up fees, it's about $60.00 - $74.00 a month (two adults and a kid for $74.00).
There is also the crazy brand-new YMCA. They have a fitness floor and group classes.
I know the City of Flagstaff Aqua Plex offers Zumba and some other group classes. It's discounted with a membership. Their fitness floor is small, but it's actually really nice.
The other gyms, I'd Googles. I am not sure about them. I know the City of Flagstaff park system offers quite a few classes, and their facilities are nice. Otherwise, there is the Jazzercise studio, Curves, and a couple smaller venues. Flagstaff is much smaller than other cities, and because many employers up here offer their own facilities (NAU, GORE), there isn't such a demand for gyms here.