The airport is about 15km (9 miles) from the town center, the ferry dock is about a mile (2km) farther. By taxi, it's probably about 15 minutes. I didn't take the taxi (took the bus from Kirkenes to the airport), but I think the fare is NOK 350-450, depending on time and day of the week. Consider the Flybuss(airport bus) -- they're normally timed to meet the planes, and, if your plane is timed to meet the Hurtigruten (which I assume it is by the nature of your question), the bus will stop at the ferry terminal itself. Bus fare is NOK 70 per person. You can also call or email Hurtigruten for directions -- I expect they're quite eager for their customers to make it to the ship... :)
If you're arriving earlier than the boat, be warned: the "terminal" is little more than a dock, with no facilities whatsoever. If you're arriving significantly before your boat's arrival, consider going downtown. The tourist office will store your bags (for a fee). The ferry dock is about a 15 minute walk (or 5 minute taxi ride) from the tourist office (taxi company is right next door).
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