201 Live Oak Street
To clear up a few rumors that still float around even today, the Grapevine, a defunct restaurant near the intersection of Texas Avenue and University, was not and was never at Saber Inn down the street (EDIT 6/12/2018: actually, that may have been right all along--more later). It was, however, not located at its current place, from 1974 to 1980 it was at 315 Texas Avenue, a long-gone address that was shared with Senter-Piece Flowers.
In 1980, the current restaurant was built and owned by Patsy Perry (Zobel), running up until 2001 when Patsy (now Patsy Zabel) retired retired after nearly three decades [archive]. The restaurant briefly reopened under new owners (as mentioned in the KBTX article) and it did in fact open (in the original 2013 version of this article there was a Battalion article from 2004 entitled "Fresh from the Grapevine", but they removed it and I can't get an archived replacement article), if briefly, probably gone by mid-2005, if that.
Normally we would just put up an ad (as seen above) but today, we're presenting (and this is something I've worked out) real recipes from The Grapevine. The dressing, the potatoes, and the cheesecake have all been released on a Facebook group, and they're here now. (Yes, I got permission and yes, the link does in fact work!)
I also acquired a partial menu from late 2000 (with the last price increases in place--a typical entree held a cost of about $8.50) but I decided against putting it up except on request.
This blog reports it was "Lighthouse Christian Church" for a while after the closing of the Grapevine. The blog talked about said baked potatoes in great length, which I have reproduced here. I was going to leave a comment, but comments are closed on that post. Their loss, I suppose. I don't know how long Lighthouse was there, the blog was published in June 2007, but June 2007 happened to be when the current tenant, the Rohr Chabad Jewish Center, opened its doors for the first time.
Updated July 2017 with new photo taken this month, clarification of when the current restaurant opened, redoing links, further details on chronology, and integrating the October 2013 update.