Oslo is one of the most beautiful, clean and unique cities I've ever been. The people are extremely nice, though often reserved, and the food and wine is exceptional. Price-wise you can compare it to New York. It's easy to lose track of what you're spending but you could also do Oslo on a budget quite easily. For example, hang out at the Mathallen Food Market and enjoy a Salmon Poke bowl with a local beer. Here are some of my favorite restaurants, hotels, bars and things to do: 
Hotel: Grims Grenka
This hotel is sort of funky/retro but super spacious, clean and unique. The staff was great and the bar and restaurant had great menus. 
Boat tour: We took an old bait boat from City Hall Pier 3. Her name was Helena and she had a full bar and delicious, fresh-caught shrimp. This was the perfect, sightseeing cruise at under 2 hours.
Vigeland Sculpture Park: This large sculpture park is perfect for a long walk or picnic. The 200+ sculptures by Gustav Vigeland
Viking ship museum: Check out these (huge) ancient ships and viking artifacts, it's pretty outstanding.

We had a fantastic lunch at Skur 33 β€“ an inventive Italian-fusion spot with just-caught fish, pizza, and homemade pasta. We hear the dinner is just as good.
Kontrast is a chic, Michelin-star, fine-dining spot that offers an extensive Chef tasting menu and a phenomenal wine list. It's pricey but a fabulous experience. I had some rare wines I still can't stop thinking about.
Kverneriet has some amazing burgers (all kinds, including the Thai which was a favorite), along with an extensive cocktail list. This place is great for big groups and very centrally located. 
Brutus is natural wine bar outside of town in the Kampen area. It's very chill and super hipster. They give you a list of wines by the glass and if you're interested in a bottle they escort you to the cellar to pick one. Gotta love that.
Mathallen is a huge, international food market with options for days. You can sit at the Champagneria with a glass of wine or cruise over to the Spanish tapas bar, just don't miss the local fish guys with the best smoked salmon you'll ever try. 
Arno is a small, semi-traditional iItalian restaurant near Mathallen with delicious pasta and a phenomenal meat and cheese platter. 
Mantra is your go-to for Indian Food, near the best shopping street, Karl Johans. It's packed with locals and feels very luxurious while not too expensive. 
Miss Sophie is a really cozy brunch or dinner spot in a happening area. The interiors are extremely unique - pink velvet chairs and palm tree wallpaper. At least go for a cocktail and a snap.