Moscow is about 20 minutes away from WSU, weather dependent.
Moscow and Pullman are both college towns, so if one university doesn't have much going on, there's sure to be an event of some sort at the other one. You just have to pay attention to what's going on and plan ahead. Both cities have farmer's markets that are pretty popular, we have an annual lentil festival, county fair in September . . . And a whole lot of bars. Pullman has a bowling alley! There's hiking trails nearby, skiing not too far away, campgrounds, that kind of thing.
What type of research are you interested in? Do you have a lab or mentor picked out to work with?