Graz is a great city and you will not starve!
I find two restaurants very interesting and consistently good.
Santa Clara in Burgergasse 6 is something like an italian tavola calda, with good cooking based on local products, with a focus on seasonal game, poultry and vegetables. They have a quite wonderful buffet with anti-pasti. Tables are small and offer little comfort, but the food is good. They serve typically two or three main courses, announced as the daily specials by the waiters.
They have an oven which lends itself to slow braised dishes - like grilled stuffed onions or lamb shanks.
Service is a bit chaotic but not hostile nor pushy. The noise level can get a bit uncomfortable. I mention this since it is not a problem in summer when you can sit outside.
Landhaus Keller next to town hall is a typical styrian restaurant with reliable food based on good products. Again a place with a quite magical terrace in summer. Not creative, just perfectly executed traditional fare - cooked sliced marinated beef with salad and herbs. Excellent local wines.
A recent development which I tried only once so far is a very surprising thai place. Krua thai on Griesplatz used to be your average thai fast food, but five or six months ago they went bust. A thai lady has bought the place and now cooks her own home and family food with astonishing results. This is the best thai food I had in Austria.
One more thing: on the square near the opera house is a morning market where local farmers sell their goods. You should buy some of the produce there, like the purple-black beans - Kaeferbohnen - and the totally divine green-black oil from roasted pumpkin seeds. That stuff turns everything it touches into gold. Look for producers called Zurks and Kiendler.
Wine in Styria is heavenly - look out for a producer called Lackner Tinacher from Gamlitz, specially his Sauvignons called Steinbach and if budget is not an issue the single vineyard limited selection from a single plot called Welles.
Thanks for your prompt answer and suggestions!
Actually, I should have been more specific in my question, but I chose not to, since I could not find many posts about Graz.
What I am essentially looking for are medium-priced styrian restaurants, both traditional and more creative ones.
And, since you brought up the Thai restaurant, I've seen that there are three Indian restaurants and a number of Japanese and Chinese ones. Are there any particularly good ones?
Lastly, I know that in Graz the Cafè tradition is not so big, but I'd like to know if there are any good places, and also nice Kaffee und Kuchen spots.
Thanks in advance!
Both places I mentioned fit your description, with Landhaus Keller being the more traditional. Outside Graz but in reach if you had a car would be two restaurants that are both traditional and inventive. Not exactly medium price though. Look up Wirthaus Sattlerhof in Gamlitz - a restaurant associated with one of Styria's best winemakers - and Landhaus Oswald in Gross Florian.
Sorry, I tried none of the Graz indians nor the chinese. I would be very reluctant to try the japanese. Here in Central Europe, we are not known for our seafood and rice :-).
Your intuition about the Kaffeehaus culture is right, but there are stunning deserts. Styria is famous for its fruit, with some apple, pear, berry and apricot varieties enjoying a status usually reserved for top class vines.
Sorry this is late, but for the record : After a couple of days exploring Graz, there are quite a few smaller cafes in Graz. Some worth mentioning are :
cafe Kaiser Joseph next to the Farmers Market, limited pastries but very good coffee and smoke free,
cafe Weitzer in the hotel, old school type of place which I really like, smoking only and
cafe Sacher, a spinoff from the famous Vienna location with smoking and non smoking sections and they offer the famous torte!
All are very busy at lunch hour, so plan a mid morning or mid afternoon visit if you can.