Bottom air intakes are hindered by several things, reducing their effectiveness.
-Most cases have their 'floor' sitting too close to the surface that the user will place the case on, i.e., the case feet are too short. I think this is the largest shortcoming for bottom fan options in cases, up there with cases using solid front panels. Fans need some breathing room to be effective.
-The bottom filter and area should be cleaned more frequently than the other sections of a case, as dust is drawn in, settles, and collects more easily at the bottom. Might even be better to go without the filter; I mean, if I gotta clean it more often anyway, might as well make it a little easier for air to get in...
-Psu cables: The cables beneath the psu shroud(if present) restrict bottom air intake further. Psu itself also gets in the way.
-Size and shape of the grilles that air pass through. Larger spaces doesn't restrict air as much.
[Most of the above is from my experience with a Phantom 820; it doesn't have a psu shroud.]
For your actual question:
-Lian Li Lancool 216, Lancool II Mesh: the side vents lining up with the shroud was a good idea, IMO.
Montech Sky Two is set up similiarly. Antec DF700 Flux, has something like that, but the surface area available is much smaller.
-Thermaltake Core P3: pretty much an open case.
These all appear around $100. Below that, there really isn't anything.