I'll add onto what other have said...
If you only have time to seek out one spot, go to Forever Young. It's by far the most organzied and interesting record store in the metroplex.
I'm a big fan of Half Price Books (and I make a weekly or bi-weekly trip to the HPB near my house) but it's hit an miss, and probably nothing that you wouldn't find (out of sheer dumb luck) near where you live. Great stores if you're a local, but nothing to seek out (unless you're in town for a while and looking for evening adventures). Albert is right - the out-of-the-way HPBs in older suburbs yield the best vinyl.
I haven't been to Bill's Records in several years, but every time I've been I've found it to be *WAY* overpriced. However, they do have a ton of stuff and would be a place worth seeking out if you are in town.
Another place I stumbled upon a few years back is Books & More in Denton, Tx:
Books & More
1626 W. University Dr.
Denton, Texas 76201
I had found this place a many years ago by accident, but didn't pay attention to how I found it (I was just driving around in a new area). Well, I came upon it again in 2006. Great selection of interesting (used) vinyl. For example, multiple linear feet of Beatles releases (various releases and conditions). The vinyl is sourced through Cliff West a.k.a Record Hound (email@example.com). Pretty easy drive - exit 469 east (just north of the I-35 split).
Mind you, *none* of these places are anywhere near eachother. If I had to prioritize, I'd hit:
1. Forever Young
2. Bill's Records
3. Books & More
And whatever Half-Price Books is nearby. I have not been to Record Town in FT. Worth, but that may be an adventure for this weekend.