Hate to say it, but a lot of bars in the fort worth area are heavily oriented to select crowds. One will be jazz, another will be country, another will be indie/hipster. There are several in Arlington with a more relaxed crowd, but most places usually have a select crowd or a bunch of young people. Lots are dance oriented. It's not like pappys or no name lounge here in lc. I am from the area, and will give my mom a call as she goes out fairly often with her new boyfriend.
Anything you would prefer to stay away from other than the nightclubs?
Billy bobs is a country music place/night club depending on the night you catch it.
There are several bars in and around Houston street in ft worth.
I wasn't 21 when I lived in DFW, but I'm sure this will help you.
bars near omni hotel fort worth - Google Search
sammich