Hauptbahnhof take exit (stairs) to Koenigstrasse. At the top of the stairs - street level - look on your right and follow the aroma. A simple white crepe stand. Very crispy crepes with various filling to choose (both sweet & savory). Ham & cheese, banana & nutela, rum & sugar - yumm.
Koenigstrasse is pedestrian only shopping with stores. It takes you to the Schlossgarten and Schloss-strasse. Plenty to see and explore. Common food stands are Pretzel and Wurst.
If you like making your own sandwich, try deli stores - buy 50-100g cheese slices or cold cuts. It is not uncommon to buy small quantity. These item don't keep well in home fridges, so people buy 2-3 times a week. Same with fresh bread or buns. Find a bakery or two that you pass by everyday and get fresh baked buns or loafs. If loafs are big, ask for 1/3 or 1/2.
The year-round market - indoor - is also in the area. The insignificant building can be easily missed. Anything that says marktplatz - has plenty to eat and see.
Oh - don't miss the icecream. The scoop is small - thus you can try a variety of flavours in one shot. Ein Kugel (one scoop), zwei Kugels, oder drei Kugels.
"bon appetit" magazine of Dec 2009 suggested:
Feinkost Boehm, Kronprinzstrasse 6, 049 711 22 75 60
Cafe Nast, Esslinger Strasse 40, 049 711 23 89 70 - sauerbraten with homemade spaetzle
Weinstube zur Kiste, Kanalstrasse 2, 049 711 24 40 02 - Maultaschen (schwabish food)
Gasthaus zur Linde, Sigmaringer Strasse 49, Moehringen (suburb), 049 711 719 95 90
Don't miss the Daimler & Porche Museums.
There is a large Turkish population. Their doner is like shawarma. Their garlic lamb sausages are delicious.
If your stay is in the fall, the German celebrates harvest with new-wine and Zwiebelkuchen (onion-tart/pie). It's like north american pastry pie with onion filling - it's delicious.
Hope this helps.
You sound like a native, knusprig! I wonder if you know of a very good restaurant out near the airport and its hotels. We have to stay there because of attendance at a large exhibition. Any help would be appreciated. I'm not too keen on hotel eating, especially if the company is paying!
Try the Speisemeisterei in Hohenheim, close to the university (http://www.speisemeisterei.de), it's not far from the airport (taxi). A bit further away, but definitely worth the drive is the Wielandshöhe (http://www.wielandshoehe.de) with great views of Stuttgart (BTW both places need reservations).
In Stuttgart itself try Bierhaus West (http://www.bierhaus-west.de), the food is simple but good (try the Rostbraten!)
i will second the Wielandshöhe recommendation. probably the best meal i have had in Germany (and despite the common notion that Germany is all sausages, pork hocks and saurcraut, Germany has a lot of great food!). we took public transport to get there, although i don't know exactly where downtown, but there's a little tram that runs certain times. later in the evening, you can pick up a taxi that is the same price as the tram, back to the downtown location.
No, I'm not from Stuttgart, older siblings & their families live in the area. Sorry, I don't have info about airport area though I passed almost all the time.
Fellow Rosenbeg mentioned Speisemeisterei close to university. In the 80's, Uni (that's how the locals refer to) cafeteria served good food at reasonable price, various sandwiches and hot foods. Not sure if they still do the same.
The well-known Schwabish food are: Maultaschen - a mixture of ground beef, leeks wrapped in thin dough, served with hot broth. Spaetzle is their noodle. Perhaps the hotel staff can direct you to good restaurant that serve these.
Make sure your camera is ready for the most unique airport car parking building (with large sign Bosch). It's above - across the busiest freeway, built without closing the highway.