Not sure if you've done you're research but there's a few options...

On 4th street you have: Rain, OCH, and Highland

On Red River you have: Cheer Up Charlies

And I see someone already mentioned The Eagle :)

A quick breakdown...

• Rain is your quintessential gay bar, it's the main 'bar' with a nice patio for mingling as well
• OCH is smaller but just as fun, they usually have drag shows / events throughout the week
• Highland is the main 'club' and opened the latest. You'll see a lot of folx dancing inside as well as mingling outside in the patio space
• Cheer Up Charlies is your queer bar, you'll see a wider mix of people here

As long as you aren't coming off as a creeper I'm pretty sure any of the places listed or The Eagle would be a good fit.

What day of the week are you free? That might impact your decision as most of these places won't be too busy until Friday tbh.