Alaska does not impose a state sales tax, but individual cities and boroughs have their own taxes. (Anchorage has no sales tax.) In addition to local taxes, a hotel tax is often applied to your hotel bill. Rates are variable, generally ranging from 2% to 12%.
You won't have to pay any departure taxes if you're flying within the United States. Vancouver's airport has a departure tax of C$5 for flights within British Columbia and the Yukon or C$10 to U.S. destinations, payable at automatic ticket machines or staffed booths before you board your flight.