There are three places that are on almost any list of best places to eat in Bariloche. 

Cassis:  Located on Lake Gutierrez about 15 minutes from downtown, this sophisticated four-star restaurant has paid a great deal of attention to details and design.  Trendy, but a bit on the pricy side, you should try to get there early enough to see the sunset overlooking the lake.  Non-smoking, Cassis tailors to upper-end visitors and locals alike.

Boliche de Alberto: Now with four branches, Alberto continues to be recognized as the best steak house in Bariloche. Large portions, reasonable prices, and excellent quality means you should get there early to avoid the occasional long wait times.  Three downtown locations (one specializing in handmade pastas) and one in Playa Bonita, this is the place for an authentic Argentina asado.

Familia Weiss:  Regional food in a log cabin environment.  The Weiss family is well-known for its smoked meats, fondues, specialty beer, and family-atomsphere.  Located downtown on Palacios Street, you get a true taste of Bariloche heritage and local cuisine.

Other recommendations:

Map Room: An English style pub and restaurant, the Map Room is popular with locals as well as travelers.  Great quality food, and the only official American Breakfast (eggs, bacon, hashbrowns, OJ) in the city. Offers a wide variety of mixed drinks and excellent service, and has a daily happy hour.

Jauja:  Another fine example of regional foods. Downtown location, and not to be confused with Jauja ice cream (also excellent) or the Jauja take-out.

Berlina: 12-km outside of town, this newer brewhouse is competing quite well with its better known neighbor, Blest. A young feel, and six microbrews on tap (all brewed on-site) makes Berlina a good choice for couples looking for a nice escape from the downtown scene.

Fonda del Tio:  Popular with locals for its hearty portions and reasonable prices, this is truly a taste of Bariloche.  Nothing fancy, but great for people watching without breaking the bank.

Fast food: Next to the Centro Civico there's Morfy's, or try the shopping mall at the end of Moreno Street.  Another cheap downtown option is Santana right in front of the artists market near the Centro Civico.  For pizza try Mundo or Vogue.