Wineries do not serve dinner. The exception is the Besenwirtschaften where the wineries are allowed to serve food as long as the new wine lasts. They advertise this by placing a Besen (broom) outside. August is probably too early for this. Basically, you share tables with others usually in the owner's dining room or outdoors. The new wine (red or white depending on the winery) is served by the pitcher or Viertel (1/4 liter glass). The food is the good local Swabian food which is usually quite inexpensive. By the time you leave, the others sharing your table are now life-long friends.
We like the restaurant at the Hotel Elefanten in Lauffen am Neckar ( lauffen.de/website/…hotel_elefant ) which is a very pleasant wine town along the Neckar River not too far north of Stuttgart. Lauffen ( www.laufen.de ) has an excellent very small completely walled oldtown. Their food is very good and ask for them to recommend some Rolf Willy ( www.rolf-willy.de/willy/index.php… ) wine to accompany it. The winery is in nearby Nordheim a few kilometers away, and all of their red wines are excellent and it's well worth visiting to purchase a few bottles and sample their wine. It is near the middle of Germany's best 100 wineries and is our favorite one. Another winery in Lauffen is in the top ten.
Slightly closer to Stuttgart is Besigheim ( www.besigheim.de ) which was recently voted Germany's most picturesque wine place. We've never eaten there as Lauffen is just a few kilometers away. Just to its east at Hessigheim ( www.hessigheim.de ) the terraced Neckar River vineyards are at their highest and most extensive.
Also, at the end of August is Stuttgart's Weindorf (Wine Village), www.stuttgarter-weindorf.de , probably Germany's most attended wine festival, in the center of Stuttgart ( www.stuttgart-tourist.de ) where you can sample the local wine along with the good local Swabian food. As Germany's largest city with vineyards, which are extensive at that, you can take pleasant walks through the vineyards with wineries and places to eat along the way ( www.stuttgarter-weinwanderweg.de ). The walk through the vineyards from Obertuerkheim to the Wine Museum in Uhlbach is particularly nice and scenic with many panoramic views. There are several good restaurants within a block or two of the museum.
For a very good meal in a Weinstube with wonderful ambiance, go to Kloesterle in the Bad Cannstatt part of Stuttgart. It is in Stuttgart's oldest building which formerly served as a convent, hence the name. A nice intimate place to eat there is at the table up the short stairway that overlooks the restaurant below.
Note that Stuttgart is at the center of the Württemberg Wine Region, and most of the wines produced unlike the rest of Germany are reds.