By plane
From Narita Airport, the fastest and most expensive way to reach Utsunomiya is to take the Narita Express train to Tokyo Station and transfer to the Tohoku Shinkansen Yamabiko, Nasuno or Tsubasa service 2 1/4 hours, ¥7800.
From Haneda Airport, take the Keikyu Line train to Shinagawa, then the Yamanote or Keihin-Tohoku line train to Tokyo Station. From there, take the Tohoku Shinkansen about 1 3/4 hours, ¥5200. A cheaper trip is to continue up the Yamanote to Ueno station and change to the JR Utsunomiya commuter line 3 hours, ¥2290.
Separate Airport Limousine bus services - each called the Marronnier - run between JR Utsunomiya Station and both Narita Airport 2 3/4 hours, ¥4070 and Haneda Airport 2 3/4 hours, ¥3500.
By train
Utsunomiya is a major train hub served by the Tohoku Shinkansen Line, JR Tohoku Main Line, Tobu Nikko Line and JR Utsunomiya Line.
Tohoku Shinkansen Yamabiko, Max Yamabiko, Nasuno and Tsubasa trains depart from Tokyo station about three times per hour, with more trains during the evening. The ride costs ¥4800 and lasts just 50-55 minutes.
Direct runs on the regular Tohoku Main Line depart from Ueno station 3-4 times per hour. The trip takes about 1 hour and 40 minutes at a cost of ¥1890.
There are also hourly departures on the Shonan-Shinjuku line from Shinjuku station, reaching Utsunomiya in roughly the same time it takes from Ueno, and at the same price.
JR Nikko Line trains, appropriately bound for Nikko, depart from Utsunomiya.
Tobu line trains run to Tobu-Utsunomiya station from Tochigi every 30 minutes or so. From Asakusa, you can reach Utsunomiya by Tobu rapid train, changing in Shin-Tochigi. This train is typically longer 2 hours and less convenient than it's JR counterpart, but about 500 yen cheaper for one-way fare 1160 yen.
With the exception of the Tobu line, all of these trains can be used at no charge with the Japan Rail Pass.
By bus
Kintetsu operates the Tochinoki overnight highway bus service from Osaka and Kyoto to Utsunomiya Station. It takes 10 hours from Osaka and 8 1/2 hours from Kyoto and costs ¥11000 and ¥10400 one way, respectively. This service has been spotty with suspensions; it is usually cheaper and more reliable to take a train to Tokyo Station or Shinjuku station, then to ride a bus to your destination from there.
Mito, the capital of neighboring Ibaraki, has highway bus service connecting with Utsunomiya, with departures hourly in either direction.