Near Trondheim:

Røros: Old village on UNESCO’s world heritage list
http://www.worldheritageroros.no/
2 hrs drive southeast of Trondheim

Northern Norway:

Take a cruise along the coast of northern Norway. We recommend a trip from Trondheim to Tromsø with a return flight (Typically 3-4 days).
http://www.hurtigruten.com/

West Coast:

Known for beautiful fjords and mountains, the west coast of Norway is a turist hot spot. A suggested trip with rental car is as follows:
Day 1: Trondheim-Dombås-Trollveggen-Trollstigen-Geiranger
Day 2: Geiranger - Hellesylt by ferry (sightseeing) – Ålesund
Day 3: Ålesund – Molde – Trondheim
Extra day(s) can be spent in Geiranger and Ålesund

http://www.trollstigen.net/
http://www.trollveggen.net/
http://www.visitalesund.com/

You could also see the west coast by cruise ship. We recommend Trondheim-Bergen by ship one way and by plane (or car) the other way. Or why not go by ship from Trondheim to Bergen and fly home from Bergen.
http://www.hurtigruten.com/