It is almost never better to target colleges that do not have a GMAT requirement.
See, there is a reason behind applicants working twice as hard to get admitted to a top school. Some even wait a whole year is they get rejected and apply again, the reason being a top school can give you a certain level of advantage in regards to exposure and opportunities that other schools can’t. And most top schools require a GMAT.
Hardly ever, a top school would allow a GMAT waiver, but the student would either require to fit a few pre-set conditions or have an exceptional profile.
If you decided to apply to a school that simply does not require a GMAT, you’ll automatically remove a lot of good schools from your list.
I would suggest trying to improve your GMAT score though. Most applicants have attempted the GMAT multiple times before filling in their applications with their desired scores. Find a good GMAT coach if you must to help you score better.
If all your efforts of scoring better on the GMAT fall short, you would need a good admissions consultant. A lot of applicants with your GMAT score and profile get admitted to top business schools every year. While they hit the bull's eye in their first round of application, others that don’t make it will settle for whichever school they get into next.
Although, I can vouch that most applicants with an admissions consultant get the advantage of working with someone that knows how the system of b-school applications works.
Whether you heed my final advice or not, do apply to good schools and work on your application meticulously instead of applying to schools that don’t require the GMAT.