Where are fun spots for 20-something year olds to hang out?

You should probably hang out in Uptown Dallas (McKinney Ave) and the Knox / Henderson area. They are close to each other and right by downtown, (but not in downtown). These are going to be the trendy areas, if that's what you're looking for. I no longer live there, but off the top of my head I used to like The Porch, Coal Vines, Fireside Pies, victor tangos, The Social House Uptown - Routh, Gloria's Restaurant, and The Quarter Bar

If you have time and its not too cold, you can take a walk along the Katy Trail (Dallas) in this same area. 

6th Street Bar

I like to go to Goodfriend Beer Garden and Burger House in Lake Highlands.

If you like pubs, Trinity Hall Irish Pub & Restaurant and Dubliner.

For alt-country, jazz and music you won't always see at traditional spots, check out the Twilite Lounge.

For upscale Southern, check out Hattie's in Oak Cliff.

The best barbecue is at Pecan Lodge (usually a two hour wait in line) or Lockhart Smokehouse (in Plano or south Dallas).

For movies, check out the Alamo Drafthouse Cinema; stay away from Cinemark and AMC and don't let any of the Studio Movie Grills fool you. If you want alternative / indie flicks check out the historic Texas Theatre (where Lee Harvey Oswald was arrested).

A lot of the younger crowd hang out in Uptown around Union Bear.

come on over to Fort Worth!   Sundance Square is part of the best  downtown in the US; lots of bars,restaurants, cafes.  Check  schedules for the Bass Performance Hall, Jubilee Theatre, Circle Theatre, Stage West Theatre,  

Our restaurants are less expensive, and events at the Bass are less expensive than at the arts venues of Dallas 

Just west of downtown is the W 7th St neighborhood   sometimes  called SO7.  Another crop of cafes, bars etc.  In this area are located five great museums.  

Just south of downtown is the W Magnolia Ave Restaurant Row, with a wide variety of eateries and bars; many of which seem to attract people young enough to be my children.  

North of downtown is the Fort Worth Stock Yards which is all about the cowboy experience; dance clubs, bars, Texas food, Billy Bob's Texas and tons of Western Wear stores.