I'm probably the only person who didn't know about this place, as it's kinda famous. Not only has it been around forever, in 2009 Texas Monthly magazine declared the cheeseburger here the "best in Texas." (I think this infuriated a few folks who could not believe a hoity-toity wine bistro grabbed that kind of prestigious award.)
We sat in the tiny, but cute bar area to enjoy happy hour. Happy hour here is a total steal because wines by the glass are half price AND they have a great happy hour appetizer menu.
On Mondays, happy hour is extended until 8 PM. Their calamari has won awards and is served in a delicious spicy sauce. The cheese plate was also great.
We stayed in the bar area and ordered the famous cheeseburgers. Things you should know about this burger: it's huge, it's expensive (as burgers go), it can be split for a $1.50 charge, it's only available on Sundays and Mondays, it really does taste amazing.
I can't wait to head back to The Grape sometime soon. It's cozy, cute, and even cost-effective if you get their specials. Here is their website.