Visit Utrecht in the Netherlands. IMHO, it has a nicer atmosphere than Amsterdam, and there's plenty to do and to see (I especially like the area around the Dom, which itself is a beautiful tower/church).

About the weather: apparently the Netherlands is notorious for its weather patterns (or so international students I talk to here tell me, I guess I'm used to it), which can turn from a beautiful sunny day to colder and shower-y weather the next. Just don't expect a completely sunny stay