The Steak 'n Egg Kitchen was in this building on the bank of Gills Creek across the street from Trenholm Plaza and in front of Forest Lake Park. Commenter Lisa B's parents ran the restaurant (and another in Cayce), and she has an interesting rememberance here.
What I remember about the place is that it had a counter fitted with round, floor-mounted, stools on which a kid could twirl for as long as a parent could stand it and unpadded booths, like at the Waffle House or Huddle House lining the outside walls. I don't remember much about the menu, though I think it inclined towards hearty breakfast and lunch fare, but I do remember one item in particular. We didn't get to go there often (and in fact generally ate only one meal a week 'out'), but when we did, I had to have "Black Bottom Pie". I don't remember what was inside the chocolate cracker crust, but whatever it was, it was good! I think it's rather interesting that with the Steak 'n Egg Kitchen, there were at least three lunch counter operations in this block of Forest Drive. The other two were Liggett's Drugstore (later Ligget Rexall) at Trenholm Plaza and Campbell's Drug Store at the other end of Forest Lake Shopping Center. All three are gone now..
I'm not sure how long the Steak 'n Egg Kitchen lasted, but I'm pretty sure it was gone by the time I started college in 1980, and think it was in fact several years before that. This article from 1987 says that the chain still had 130 units then, but that it was troubled and that the new owners were attempting a turnaround. I don't find a corporate web site, so I'm guessing it didn't work. Anyway, after Steak 'n Egg Kitchen closed, another restaurant set up shop briefly in the building (which was remodelled). I can't recall the name of the place, but I got the impression that it was family run, and it had home-made raw fries. I think there was a non-retail business after that, perhaps an insurance office or some such and then the current tenants arrived and split the building. I've bought brandy & rum for cooking from the liquor store, but I don't know anything about the other two outfits. At any rate, none of them have Black Bottom Pie..
UPDATE 30 Jan 09:
Here's the old Harden Street location (mentioned in the comments). It's now El Burrito.
UPDATE 14 July 2012: Added the full street address for the Forest Drive location, and added the "Dobbs House" name to the post title. Also added some tags.
UPDATE 11 October 2013: Here is a great picture of one of the incarnations of this location. Thanks to commenter Dennis for ferreting this out!