Niste be careful applying for MBA schools that don't require a GMAT. I don't think any Graduate Business School accepts GRE in lieu of GMAT (None that I am aware of but I could be wrong). But getting back to the point. A school that doesn't require a GMAT wouldn't be accredited by the AACSB which means finding a job  after graduation is going to be a pain unless you know a lot of people in the industry. Its always a good idea to look for schools that have been accredited for a while and are ranked among top schools for certain specializations. You don't need to go for a Harvard MBA, or Sloan MBA but definitely look for a school that at least has good ranking for certain specialization. For example: University of Florida has a very good Consumer Behavior specialization, whereas UT, Austin's MIS is top rated. Babson College in Wellesley, MA is considered to be the best school for entrepreneurship. With a good recommendation, a good GPA and GMAT score you may secure a full or partial  Graduate Assistantship. They are pretty helpful  because most good schools  will cost you  a lot for an MBA program.

But if you do need a school that doesn't require GMAT for an MBA, the one I know in the east coast is Johnson & Wales, Providence, RI. I am not sure if this has changed because I am taking about 2001-2002. The students there had a saying "When everything fails, there is Johnson & Wales". It was big safety school for a lot of international students who hung in there to keep their status while applying for good MBA schools. It was cheap and easy to get into.

Good Luck!!!!!!!!
"People go to Undergraduate school for a job, but people go to Graduate school for a Profession" so choose wisely......