In Houston, TX for about 6 months or so and wondering if any of the wine stores here have any older vintage wines? Have only tried the big Specs so far.
Nothing of tremendous age is available retail. Houston Wine Merchant goes back a few vintages, but you’ll not find 90s burg on the shelf anywhere. Pay a visit to Pappas steakhouse for that 
I was wondering the other day - is there any relationship between “Houston Wine Merchant” and “Austin Wine Merchant”?
No connection- two separate owners, and AWM was in existence several years before HWM came along.
To the OP- Spec’s downtown is one option. They have good cold storage upstairs, and if you ask sometimes they will take you up there to look around (or they used to- not sure about now.)
Richard’s on Kirby is also a good place to go- they have a large cold room in the main store and they keep some back vintages of higher end Bordeaux and Burgundy. A small selection, but trustworthy on storage.
I am not sure HWM deliberately maintains any older stocks- but they are good people and worth a visit.
Back in Monsterville days, the Central Market in River Oaks had some nice older vintages, including DRCs, in their wine cabinets. I am pretty sure anything DRC is long gone, as is Monsterville, but still worth a look. Our main Central Market in Dallas keeps a few older top vintages on hand at all times, and so Houston might as well.
I have not been in several years, but the Tasting Room would get the occasional DRC allocation plus keep some top Bordeaux on hand. All kept in proper storage, and as the wines sold slowly- they would often have bottles with a few years of age on them. It is a restaurant and retail operation- so anything they serve you can also buy and take home. Again- things might have changed, but still worth having a look around the place.
And yes- for just buying off a restaurant list, second the vote for Pappas Bros. Steakhouse. Here in Dallas, they seem to have slowed quite a bit on newer vintages, but still plenty of older stocks they bought years ago and have stored well. Picked over for many top vintages, but the reality is that many top wines are ideal for restaurant drinking at 10-12 years of age from the lighter vintages, and you will find those in droves plus at prices that are often at or below current auction since they have not been aggressive about raising their prices lately.