My mum and I stayed at The Hampton Inn and Suites near the Space Needle (it was last minute about US$120) - it was my first trip to Seattle and the hotel was lovely, huge rooms and comfy beds. We booked a taxi to collect us and drop us at the terminal - no probs, about $10 - $20!
Even when we got off the boat in Seattle there were plenty of cabs.
Another great feature was free internet access in the foyer.
Enjoy your cruise!