I'm not sure of a good way to find schools that don't require mGRE, but there are quite a lot of quite good schools that don't. I would say to just look at schools that interest you and check if they say the mGRE is required. It may not be fast, but it's worth it to spend time on this decision!
Also, if it is feasible for you, schools outisde of the US mostly do not require GRE scores of any kind. For example, in Canada, I'm not aware of any program that requires it. Keep in mind that if you were to go anywhere other than the US straight from undergrad, you would be looking at masters programs. In Canada at least, almost all masters programs are funded, unlike in the US. Also there usually is a research component (vs. masters programs in the US that are mostly course based). You would then go on to a PhD program, which if you stayed in Canada, is typically 3-4 years instead of the usual 5 years in the US.