Cruises Around the Fjord -- Båtservice Sightseeing, Rådhusbrygge 3, Rådhusplassen (tel. 23-35-68-90), offers a 50-minute boat tour. You'll see the harbor and the city, including the ancient fortress of Akershus and the islands in the inner part of the Oslofjord. Cruises depart from Pier 3 in front of the Oslo Rådhuset (City Hall). They run from mid-May to late August daily on the hour from 10am to 7pm during the high season, less frequently at the beginning and end of the season. Tickets are 100NOK ($15/£8.20) for adults, 50NOK ($7.70/£4.10) for children.
If you have more time, take a 2-hour summer cruise through the maze of islands and narrow sounds in the Oslofjord. From May to September they leave daily at 10:30am and 1, 3:30, and 5:45pm; the cost is 170NOK ($26/£14) for adults, 90NOK ($14/£7.40) for children. Refreshments are available onboard.
City Tours -- H. M. Kristiansens Automobilbyrå, Hegdehaugsveien 4 (tel. 23-15-73-00), has been showing visitors around Oslo for more than a century. Both of their bus tours are offered daily year-round. The 3-hour "Oslo Highlights" tour is offered at 10am. It costs 260NOK ($40/£21) for adults, 130NOK ($20/£11) for children. The 2-hour "Oslo Panorama" tour costs 190NOK ($29/£16) for adults, 90NOK ($14/£7.40) for children. It departs at 10am. The starting point is in front of the National Theater. Arrive 15 minutes before departure; tours are conducted in English by trained guides.