This guide uses the following price ranges for a typical meal for one, including soft drink:
Budget  Under CHF 25
Mid-range  CHF 25 to CHF 50
Splurge  Over CHF 50

Budget
Suan Long, Rail City, underneath main station, Bern, ? +41 (0)31 311 87 88. Low-priced Chinese meals, wide variety of dishes, including good vegetarian selection. Quick service and ideal if you're waiting for a train. Especially recommended if you enjoy spicy food! 17-25 francs. 
Beaulieu, Erlachstrasse 3, ? +41 (0)31 301 24 59 (fax: +41 (0)31 305 86 55). Open Mon to Thur 8AM - 11:30PM, Fri 8AM -00:30AM, Sat 10AM - 10PM. Old-fashioned restaurant serving traditional Swiss and Bernese cuisine at very affordable prices. Popular amongst students due to its situation close to the university; equally popular amongst the local workers. Definitely not a tourist restaurant - go here if you want to meet the Bernese amongst themselves. 
Pastamania, Kramgasse 49, ? +41 (0)31 318 28 28 (daniel@pastamania.ch, fax: +41 (0)31 318 28 29). Open Mon to Fri 9AM to 11:30PM, Sat 7:30AM to 3PM. Located in the same house as the Einsteinhaus, this very small restaurant serves some very good pasta dishes. CHF 18-25 for the main dish. CHF 8-14 for appetizers.
Sandwichbar L16, ? +41 (0)31 331 16 16 (info@sandwichbarl16.ch). Open Mon to Fri 8AM - 19:30PM till 24:00PM (depending on weather and people), Sat from 9AM. Cool place where you can create your own sandwiches. Very popular amongst students due to its situatin close to the university. This is the perfect place if you just want to have a snack. CHF 5-20 depending on the size of the bread. 
Sous le Pont, ? +41 (0)31 306 69 55 (slp@reitschule.ch). Open Tue to Fri 11:30AM to 2:30PM and 6PM to Midnight, Sat 7PM to Midnight, Sun 10AM to 4PM. A nice restaurant in the Reitschule complex which serves excellent dishes at affordable prices. 
Wäbere, Gerechtigkeitsgasse 68, ? +41 (0)31 311 42 58 (fax: +41 (0)31 312 20 67). 11AM to 11PM except Sun. Excellent soups, a good rendering of Swiss standards, such as cheese fondue, and an decent number of veggie choices. Many items available in half portions. CHF 14-24.

Mid-range
Altes Tramdepot, Grosser Muristalden, Bern. (Across bridge at east end of city centre, by bear pit.), ? 031 368 14 15. 11:00 - 23:00. Authentic Swiss restaurant based, as its name suggests, in a former tram depot. Good, hearty Swiss food. Range of dishes from budget price rösti to higher-priced meat specialities. On-site brewery with traditional beers available. Bench seating with great atmosphere. CHF 20 - 40. 
Café Fédéral, Bärenplatz 31, ? +41 (0)31 311 16 24. Stylish, modern atmosphere and international cuisine. Situated in front of the Bundeshaus, its popularity amongst politicians during the "Session" is legendary. Specializes in Entrecôtes (a kind of steak), but has other dishes, including vegetarian ones. 
Casino Restaurant, Herrengasse 25, ? +41 (0)31 328 03 28 (info@casinobern.ch). Located at the shore of Aere river, with a view over the river and mountains on the South. Dishes include excellent pasta with mushrooms, fish, and meats, served throughout the day. CHF 25-45 for a main dish. 
Kornhaus, Kornhausplatz 18, ? +41 (0)31 327 72 70 (fax: +41 (0)31 327 72 71). The room alone is worth a stop at this fabulously appointed mostly Italian restaurant. As one might guess from the name, the building was originally built for grain storage, but now features fresco paintings of traditional swiss scenes, events from local history, and related characters. CHF 26-45 for the main dish. CHF 9-14 for appetizers.
Schmiedstube, Schmiedenplatz 5, ? +41 (0)31 311 34 61. Open Mon to Sat 8:30AM - 11:30PM. German, French, Italian, English and Spanish spoken. This traditional Swiss restaurant is well known for its typical dishes, such as Röschti, Cordon Bleu, Älplermakkaronen. Its location in the heart of Berne (300 ft from the clock tower "Zytglogge") makes it an ideal resting stop while you're enjoying the city of Berne. 
Schwellenmätteli, Dalmaziquai 11, ? +41 (0)31 350 50 01 (info@schwellenmaetteli.ch). Terrace Open Mon to Sun 8:00AM - 24:00PM. A very nice restaurant at the side of the river Aare with a nice view on the Cathedral. CHF 20-40 for a main dish. 
Vatter, Bärenplatz 2. Grocery: 9AM to 5PM, Restaurant: 10AM to 10PM daily. Vatter is the largest of the several organic groceries in the old town, and has its own restaurant upstairs as well if you don't feel like cooking, or lack the facilities. It serves excellent beer from the Locher Brewery in Appenzelland has a balcony overlooking Bärenplatz. CHF 8-20

Splurge
Bellevue Palace, Kochergasse 3-5, ? +41 (0)31 320 45 45 (fax: +41 (0)31 47 43). Berne's N° 1 address. Stylish hotel and restaurant; has its price. Go there when the Parliament is in session, and you may very well see the president of Switzerland having lunch. 
Restaurant Rosengarten, Alter Aargauerstalden 31b, ? +41 (0)31 331 32 06. Upscale Swiss restaurant with amazing view over the city.