Your GPA is sufficiently high that it will not prevent you from applying or being accepted to pretty well any US university - but once your GPA is above a 3.5 it tends to just be marked as "good enough". A research group that would base a decision solely on a GPA of 3.7 vs 3.9 vs 4.0 would have a disturbingly irrational fetish for GPA that it would be a mark against the research group more than it would be against you!
It appears this sentiment is shared by Dr Mor Harchol-Balter of Carnegie Mellon University, where she writes (my emphasis added):
3.1 Transcript – grades and classes
When applying to a Ph.D. program in CS, you’d like your grades in CS and Math and Engineering classes
to be about 3.5 out of 4.0, as a rough guideline. It does not help
you, in my opinion, to be closer to 4.0 as opposed to 3.5. It’s a much
better idea to spend your time on research than on optimizing your
GPA. At CMU the mean GPA of students admitted is over 3.8 (even though
we don’t use grades as a criterion), however students have also been
admitted with GPAs below 3.3, since research is what matters, not
grades. A GPA of 4.0 alone with no research experience will not get
you into any top CS program. Keep in mind that GPAs are evaluated in
the context of the undergraduate program. A 3.4 GPA from a topranked
CS undergraduate program like CMU counts the same as a 3.8 or 3.9 GPA
from a less well-known CS undergraduate program.
As @Potato notes, this strong preference away from GPA and towards research may only apply to some fields where undergraduates are capable of participating in research. This may also not be true of Universities without such a very strong focus on performing research. In short: YMMV.
At the graduate level there are multiple factors considered, discussed in various and tremendous depth throughout other topics on this site (and highly recommended to be searched through!). But with that said, your GPA is more than high enough that you may now safely worry about all the other criteria that will be considered: reference letters, statement of purpose, any existing relationships directly or indirectly with professors at the institution, experience in research (or that shows potential for research), GRE score being "high enough" (just like your GPA!), TOEFL for international applicants (again, "good enough") etc.