Your 'base' will be in Longyearbyen - a pleasant and quirky little town. Free time is never wasted, as there is plenty of exploring to do and there are several small cafés and decent restaurants, many serving traditional Norwegian fare, including Svalbard specialties such as seal and whale. The tax-free status of the islands makes alcohol a lot cheaper than on the mainland - therefore, it's good value...but only by Norwegian standards! There are a number of good hotels, but do remember how far away from civilisation you are up here - don't expect valet services, plush interiors or five star facilities.
Outside of Longyearbyen there are some remarkable options - all quite un-expected - which can be integrated as part of your activities. The Ship in the Ice is an experience as memorable as it sounds, the wilderness and expedition lodges are as remote as is humanly possible and converted Isfjord Radio Station is a characterful boutique hotel to rival any in the world.