can you have fun without going greek?

If you are accepted into a sorority it shouldn't be awkward because your acceptance would mean you are liked and respected. However, you can go to parties without actually being Greek, and another way to have a social life is to become involved in activities outside of Greek that interest you

I don't plan on going through recruitment anymore. But I know greek life is a major part of the SMU community. I just want to make sure I get involved and can have a social life ha ha

I would ask you to Pleasepleaseplease reconsider recruitment. See how it goes. There are a lot of nonjudgmental girls in all the houses. Also, for me personally, I really would not be a part of my sorority if not for a variety of women, of a variety of races, who convinved me before after and during that it was a good idea. If every woman of color at smu refused to rush, I would be missing a great deal of people who are very very important parts of my sorority family. Our culture as a group would be lacking, and I really believe you can find a home.
This site shows the worst parts of the Greek system, and I promise it's a minority.
For your question, if you want a less Greek influenced place to stay, try maryhay or Peyton as dorms. Few people from those dorms go Greek since they are the art dorms. It will let you meet some people who are also not a part of the Greek system and give you an easy friend group and non-greek social life.