I think the Syma X1 is about the best fun for the money in RC, ever. It's indestructible, flies well indoors or outdoors in calm air, is agile and fun to fly. It costs $30 or so on Amazon. I love it.
I tried a couple different ways of mounting a camera under it. The main challenge with this is to get it securely attached, since there is an oddly shaped battery assembly below the main platform. It has to be very light, since the quad doesn't have a lot of cargo capacity.
This is the best I've come up with so far - it uses HobbyKing vibration mounts and some 3D printed parts. I printed them in ABS for light weight and a bit of flexibility, and I recommend that if you try it. The printed ring fits snugly around the circular frame that the control board electronics sit on and is attached with a couple zip ties. I had to slightly drill out the two unused screw holes in the circular frame.
I used an older 808 camera, which it lifts fine. There might be light enough FPV gear out there now, I'm not sure. There is still some vibration in the video - I'll probably try a little foam between the camera and platform to see if I can get rid of that. It's a fairly low frequency, since it's not causing "jello" (rolling shutter).
STL files hosted on Thingiverse here