I'm delighted to help.
You'll definitely have an amazing time at Bagatelle with flawless food and excellent service. However, if you have dined at French 2* Michelin restaurants before, you may have a more unique experience at one of the other options.
Oscars Gate is a very small restaurant (seats 20) run by a group of young chefs with experience from top restaurants around the world (including El Bulli) with an excellent and very playful 8 course (+++) menu. They got their first Michelin star this year. NOK 1095 prix fixe.
Palace Grill is not for everyone, but it is definitely an Oslo staple, that has been true to its rock'n'roll gourmet concept for years. Informal, small and intimate dining room. The serving staff has a personality (be friendly to them, or they will not be friendly to you). You order the 10 course fixed menu, lean back and spend four hours in foodie heaven. No reservations, so show up early (no later than 6, earlier on Fridays and Saturdays). They do only one seating per night, so as soon as you have confirmed that you have a table, you can enjoy drinks in their bar next door until you're ready to eat. 850 prix fixe.
Mark-up on wine will also be significantly lower at these places compared to Bagatelle.
No matter where you go, I hope you will post a report afterwards.
There are many good restaurants in Oslo, and as soon as you go a little upscale, food prices are not horrible compared to international standards. Prices for wine, though, are ridiculous.
Here are some of my favorites:
Fine dining (booking in advance is a must):
Bagatelle - French 2 star. Very expensive.
Oscars Gate - Creative with Scandinaivan, French and Italian influences - 1 star
Statholdergaarden - Scandinavian 1 star
Le Canard - French 1 star
Palace Grill - Creative Scandinavian. Informal restaurant, but amazing food - no reservations - show up at 6 and have drinks at the bar before dinner
Affordable fine dining (book in advance):
Oro - Creative Scandinavian
Ylajali - French/Scandinavian
Eik - Creative Scandinavian
Fjord - Fish
Klosteret - French/Scandinavian - very romantic candlelit basement
Ekebergrestauranten - French/Scandinavian with amazing view of the city. Take a tram to get there.
Cru - Scandinavian. Wine place with many options by the glass.
Solsiden - Fish and shellfish. Only open in summer. Great location for outdoor dining if the weather is nice. A bit expensive for the quality of the food.
Nodee - High-end Chinese and Sushi right by Frognerparken.
Alex Sushi - One of the best sushi places in Europe(?)
Dinner - Schezuan Chinese - a bit upscale for a Chinese place - always packed
Xich Lo - Vietnamese - not really fine dining, but really good
Pascal - French bistro and bakery with Scandinavian influences- good food and amazing cakes
Theatercafeen - Go for the atmosphere rather than the food, popular among financiers, artists and politicians
Beach Club - Diner - Great burgers
Brasserie France - French bistro - traditional
Olivia - Italian - good option for outdoor dining
Delicatessen - Spanish tapas - no reservations, so be prepared to drink beer while you wait. Pretty loud.
Bollywood - Indian
Rehmans - Indian
Mucho Mas - Mexican/California
Enoteca - Italian with good winelist
Rice Bowl - Thai/Vietnamese - no alcohol
Nam Fah - Thai - tasty and cheap - note that their Grünerløkka branch is only take-away