It isn’t as binary as it sounds. A lot of “need-aware” schools choose their first round of admits need-blind, and only use a need-aware process for the more borderline category in order to fill out their class without overspending on financial aid.
Your best bet is to apply to a mix of need-blind and need-aware schools, chosen primarily for fit rather than based on whether they consider financial aid status in the application process. As others have said, “need-aware” doesn’t mean you can’t get in; it just drops your odds of getting in if the school is already a reach. Make sure that a majority of your list is comprised of schools for which you are well-qualified, and you will be fine.
As far as a list, the Wikipedia page entitled Need-blind Admissions is not comprehensive, but it gives a lot of good information/examples to get you started.