The park is in Fukushima, but its a short drive from Tochigi and well worth the effort. You can combine a trip to this park with a trip to Komine Castle (which also has an excellent rose garden).
There are two main parts to the park both of which are fairly quick visits. The gardens are a classic example of a Japanese garden complete with tea rooms. Entry to the gardens is 350 yen and for an extra 500 yen you can go to the tea rooms and have traditional tea (without the ceremony) in a pretty little tea house. The tea is well worth the price, especially if you are visiting Japan or haven't experienced ocha before.
The garden is small but quite beautiful with a big lake, lots of cedar trees and little streams running through it. Judging by the photos its a good place to visit in autumn too.
The lake is quite large and also surrounded by cedar trees. Its quite beautiful by afternoon light (and I imagine morning light). There are boats you can go out on the lake in (though nobody was using them when we were there). There is not a single swan shaped boat!! You can walk around the edge of the lake. We only went a short while, but it must take a hour to walk all the way around. There is a great place to shoot the sunset from the side of the lake.
There is also a small temple at the lake though the only thing I could see to recommend it is you there is sake sampling at the entrance for a donation :-)
We strongly recommend this trip. Combine it with Komine for a great day.