Utrecht's central position in the Netherlands makes it an excellent base. Amersfoort, a medieval city with intact canals and a good museum, is just 20 minutes by train. Gouda is 30 minutes south and worth a half-day for the cheese market, the Waag, and the stained-glass windows of the Sint Janskerk.
The Hoge Veluwe National Park — the largest nature reserve in the Netherlands, with the Kröller-Müller Museum and its Van Gogh collection in the middle of it — takes about an hour by train and bus from Utrecht and makes a rewarding full-day excursion. The castle village of Amerongen and the windmills at Kinderdijk (via Rotterdam) are both feasible in a day.