My personal take:
Utrecht is lovely, has unique bi-level canals, several great museums, and few tourists. If you go, my favorites were the Centraal Museum (with quite a variety from ancient ships to modern graffiti art), the Railway Museum, and the Museum Speelklok, with music boxes and huge fairground organs (you see it with a one hour tour, on which a docent demonstrates the various music-makers). There's even a tiny red-light district, if you crave such things.
Leiden is also nice, and has the oldest university in the Netherlands. While Utrecht and Delft also have universities, only Leiden looked or felt like a "college town," with visible students. I enjoyed my canal cruise there, as well as the science museum. Did you know that kidney dialysis and EKG's come from the Netherlands? I didn't, until I went to the museum.
The Hague has interesting museums - but for me, that was the only interesting thing about it. It definitely wasn't as attractive as Leiden or Utrecht. However, if you are drawn to the Gemeentemuseum (modern art including lots of Piet Mondrian), or the others mentioned by Chani (all good), then staying there would be worthwhile.
You really can't lose, and as said, you can stay in any of these and see the others as easy day trips.