They fit in almost everything you can throw at 'em. Never used mini-towers though, personally. You can get low-profile/half-height Radeon 4650 cards by Sapphire or Asus at NewEgg.
That said, you can get a standard ATX mid-tower case for the same price from Cooler Master.
The one I use is the - COOLER MASTER Elite 310
- genuinely good case for the price. Spacious, well ventilated and easy enough to build.