From the World Heritage inscription:
The shrines and temples of Nikko, together with their natural surroundings, have for centuries been a sacred site known for its architectural and decorative masterpieces. They are closely associated with the history of the Tokugawa Shoguns.
Nikko is a day trip from Tokyo. About two hours away by train, half the trip is via shinkansen (bullet train) and the other half is via a smaller commuter train. Nikko is a small town located in the mountains and surrounded with cedar forests. Nikko is a collection of Shinto and Buddhist temples built from the 16th to 19th century.
You can walk from the train station to the temple area (I did it) but it will take about 30 minutes and the walk is mostly uphill. There are taxis and buses which can drive you to the temple site. Nikko is world famous for a small wood carving on one of the temples: the see no evil, hear no evil, and see no evil monkeys. While I was there, I saw everyone lined up to get their photos taken in front of the same building acting goofy. I had no idea what was going on. I saw the carving, and together with all the mentions of the monkeys in the stores in town, I figured it out.
Visiting Nikko from Tokyo takes a full day, but it is probably the best example of traditional shrines and temples you can see within easy traveling distance from the city.
View my complete list of UNESCO World Heritage sites.