Mom and I wanted to venture to a Czech town called Telc that looks amazing, but didn't want to drive 4 hours to see the city, so we settled on visiting Cheb for a few hours on Labor day. There really isn't much to say about Cheb though unfortunately. It is a weird town. When you first venture in, there is this huge gaudy flea market with a large Vietnamese population selling ugly purses, gaudy clothes, and cigarettes. We drove right past that area to the downtown, passing gross Thai Massage buildings. Like I said, weird. The downtown is actually pretty nice. Gorgeous mid-evil buildings. But that is about all it has going for it. Hardly any trees, and really crappy stores with chinsy cheap crap. All but one... We found a really nice chocolate store selling Belgian chocolates in beautiful tins.
I suppose the fact that it was cold (in the 50s) without much sun and some drizzle didn't help, but I won't be returning to Cheb ever again, nor can I really recommend it much for a day trip even being so close to Graf. I'd say go ahead and venture further to Karlovy Vary or Prague.