I've been to the Euro Shop in Waco, British USA, Lone Star BMW/Triumph, and RPM Cycles of Dallas.
The Euro Shop is pretty awesome. They do alot of custom work (not bolt ons, but actual mods, bobs, etc.) even on new bikes that haven't sold yet. They are a Ducati dealer too and are heavily involved in racing. They have equal passion for both brands. Lot of clothing too.
(no web site that I know of)
British USA is awesome too. They have a pre-Hinckley sales side as well. It's been a while since I've been there, but they are definitely a Triumph dealer. If I were to start a dealership, I would emulate either of these two.
http://www.british-usa.com/home.asp
Lone Star BMW/Triumph are a friendly bunch, but don't expect them to help with any mods outside of stock. They even refer such mods (even a jet change) to the Euro Shop in Waco. They have an okay selection of clothing too. Not a bad shop but I prefer the other two even though they are farther away from me.
http://www.lonestarcycle.com
RPM Cycles is famous. (I bought my Rocket here) These are the guys who restored the original Bonneville record setting bike that burned in the museum fire in England. They are a Triumph only shop. They don't have a huge selection of clothing in stock and are a relatively small shop, but these guys are a real part of Triumph history (above and beyond the restoration) and live, eat and breath Triumph.
http://www.rpmcycletx.com/
I have been to Joe Harrison when they were a Triumph dealer and, well.. they sucked a$$. I actually rode my TBS up there and started checking out a Bonneville America and a salesman asked why I would want that when I could have an ACE 750 for a bit less? Could this be a reason they didn't do well with the Triumph line?