Since many of the sites are spread out.  I would recommend renting a car or driving to Spokane.  Traffic and parking usually isn't a problem. Taxis are relatively inexpensive if you wish to choose that route instead of driving yourself, use an online fare calcutlator to test out sample fares before you decide if you want to rent a car or take taxis.  If you stay downtown and your in fairly good shape you can walk or bike to the downtown sites, Brown's addition, even Manito Park.  Realize Manito is up on the south hill so although it might not be far from downtown it can be a bit of a climb.