Buy an Oslo train pass.

Seriously. It goes everywhere and is so easy to use. See the Frogner sculpture park early in the morning with coffee before the tour buses get there ;) check out Mathallen neighborhood for beer and good food courts!

Take the ferry to Bygdoy. Boats! Stav churches. Culture. You can swim! Just about anywhere!

Watch the sunset at the Opera House (touristy but no regrets). Eat dinner at Madonna!

Stay at the Sommero if you need a swanky hotel. The breakfast buffet alone is worth it.