Harstad is a scheduled stop on the Hurtigruten coastal express — the famous passenger and cargo ferry service that runs the full length of the Norwegian coast from Bergen to Kirkenes (or back), calling at 34 ports in each direction over a journey of around six days each way. The service has run since 1893 and is genuinely useful as transport, not just a tourist cruise.
From Harstad, you can board northbound towards Tromsø (a few hours), Hammerfest, and the North Cape, or southbound towards the Lofoten Islands and eventually Bergen. The scenery between ports is often spectacular — the stretch between Harstad and Tromsø passes dramatic fjords and open coastline. The Hurtigruten is not cheap for tourists, but shorter legs between adjacent ports are affordable and give a taste of this classic Norwegian travel experience.