If all you have is a few hours here and there you will be limited to activities you can do easily from the downtown area. I'm going to further assume you don't have a car.
So here's a list of some ideas off the top of my head:
- Pike Place Market
- ferry ride to Bainbridge Island and back
- Pioneer Square strolling
- Underground Seattle tour (can be combined with Pioneer Square)
- Seattle Center and the Experience Music Project
- boat ride on Lake Union and Lake Washington (probably an afternoon event, not a one or two hour actiivity
- Uwajimaya store in the International District
- Museum of Flight
- rent bicycles and ride the Burke-Gilman Trail (weather and time permitting)
- Discovery Park
Re what to do with a free afternoon, that depends a lot on what your interests are. Shopping, hiking, guided tours, general sightseeing ????
re shopping: the principal shopping area in downtown Seattle is centered around 6th and Pine, not far from your hotel. But I think the best shopping is in downtown Bellevue - take a #550 bus from any of the bus tunnel stations in downtown Seattle. #550 buses run every 15 minutes during much of the day; about every 5 minutes during rush hour, and every half hour in the evenings.
If you like recreational gear, though, you should catch the flagship RCI store on the north side of downtown. It's awesome.
Note re downtown transportation. Until the early evening, buses are free in the downtown area (from Virginia on the north to Jackson on the south and between the waterfront and I-5).