Location can matter in some senses and not others. So can "good neighbourhood."
Proximity (walkability, close to grocery store) won out over "wealthier/lower crime area" for our last rental.
We avoided the worst areas for crime and violence and drugs, but we still picked a less-than-desirable neighbourhood. The stats said there was more car theft, schools weren't great and there were some drugs. Low violent crime though, lower arson/fire rates than the worst neighbourhoods, and good landlord. With no car, no kids, we saved $300-$400 a month over any other area.
That let us get what was important to us - walkable area, extra bedroom for roomate, good landlord, wood floors, good heating system, no pests (which is hard to find in anything cheap in that city), great neighbours.
When we went to buy, we valued walkability and good school districts and low crime. But for renting, realizing some aspects of a "good area" didn't matter to us saved us a lot of dough.