There is no shortage of hotels near the base. We would recommend looking for a place in DuPont or Lacey, which are both nice areas and are just a few minutes from the venue.
If you are interested in sightseeing a bit or plan to stay a bit longer to explore the area there are loads of things to do and see nearby.
If you don't mind driving a bit further, a stay in Seattle, Tacoma or Olympia would be of interest to you. Please do keep in mind that the Seattle metro area is densely populated and traffic can be a challenge at certain times of the day.