The great thing about Dallas is there are lots of different places to go out, but not necessarily in the downtown area itself, although people do.
As others have suggested, Uptown is a great place to go for trendy bars/restaurants/nightlife and high end retail.
If you are a fan of a more hipster vibe then I might suggest Bishop Arts in Oak Cliff or Deep Ellum, close to downtown.
The bars of Greenville and Knox Henderson are very popular, with northern greenville being a target for SMU students. Many people live in the so called M-streets because it is a quite residential vibe mixed with close proximity to some of the best food choices in Dallas.
Feel free to reach out to me and we can discuss each of these different areas and what fits you best personally.