I was looking at the different transportation options to get to the Seaport Hotel from the airport, and thought I would summarize them here for the benefit of others.

Most convenient:
Taxi - straight from the airport to the hotel. I'm guessing the total cost is around $15 + tip.

Bus - the Silver Line goes from airport terminals to the World Trade Center stop, which is about 500 ft south of the Seaport Hotel. Total cost is $1.50.

Most Interesting:
Water Taxi - Take the Route #66 bus from any airport terminal to the water transportation terminal (that part is free), then take a boat across the harbor right to the Seaport Hotel. Total cost is $10.