If you want to game the system, you need to do a lot more research. I agree that there are a lot of underrated universities that might be easier to get into. However the underrated universities will have specialities in different fields, subfields, or specific topics. My university has world class lung function group in an otherwise mediocre life science department. That trend will be replicated throughout Europe; mediocre university but contains a couple of world class research groups.
So if you want to game the system; choose a topic, research it extensively, look at the university affiliations on highly cited papers and then apply there. I don't agree with this strategy but it might work.