There are no Shinkansen stations in Ibaraki, but the Joban Line passes through Mito on its way to northern Tohoku. There is an express train called the "Fresh Hitachi" which links Ueno and the capital Mito in approx. 1 hour. The local Joban line takes just over 2 hours. The Tsukuba Express Line connects Tsukuba to Akihabara in downtown Tokyo in about 45 minutes.

The 2 major cities in Ibaraki are Mito and Tsukuba.
In Mito city, you can find the following major tourist attractions.
Kairakuen Garden - One of Japan's 3 most beautiful gardens. (Kenrokuen Garden - Kanazawa prefecture and Korakuen Garden - Okayama prefecture) Famous for its 3,000 plum trees. Visiting the Kairakuen Gardens you can also enjoy a breath-taking tour on the walkways through large stands of tall cedar trees and bamboo. Every time of the year there is a period of a specific flower blossoming. There is a hillside garden with a spectacular overlook of Senba Lake and Park. 
At the south gate of the park you can find the Tokiwa Jinja. This large Shinto shrine is dedicated to the Mito clan.
Also around Kairakuen, you can find the Kobuntei  which is a well-preserved, old-style samurai residence.
Giretsukan is a small museum on the grounds of Tokiwa Jinja houses. 
A huge rolling taiko drum, an ancient large-barrel cannon on wooden wheels,  and other items from Mito's samurai glory days are exhibited here. 

In Tsukuba you can find the Tsukuba Shrine - Notable for a huge bell and Nikko-style carvings, this shrine lies at the foot of the cable car by the Tsukuba mountains. There are also several hiking paths up the mountain, the most direct will get you to the top in about an hour. However, the longest trail offers the most cultural sights, such as a large stone Buddha.