There are many ways to take a sightseeing tour of the city... walking, jogging, boat and bus tours are available, and now even bike tours as well! The tours are offered by Bike Sweden which is located right in front of the Museum of National Antiquities (Historiska Museet). They offer three set tours. A three hour tour around the nearby island of Djurgården (500 SEK per person), a four hour tour out to the Woodland Cemetary- a UNESCO World Heritage site (695 SEK per person) and a six hour tour out to the Drottningholm Palace- also a UNESCO World Heritage site (1195 SEK per person, including boat tour and lunch). Their multilingual guides will keep you informed of your surroundings and all tours include a sandwich and a soft drink.
If you are interested in biking on your own then they offer bike rentals as well. They offer rentals for different durations... from 3 hours up to 7 days. They have different types of bikes available, like mountain bikes and city bikes. They also have children's bikes, child seats and child carriers available. Click here for a price list. For more information, check their website (linked above) or contact them at firstname.lastname@example.org
The closest subway station to the Museum of National Antiquities is Karlaplan (red line), five stations away from the Rival Hotel.