We have one day in Trondheim and I'm looking for tips on how best to spend our time. What are the must see places?
The centuries old Nidaros Cathedral where St. Olaf is rumored to be buried should be on your list.
Suki is right about the cathedral.
Other than that, I think Trondheim is not filled with must-see sights. It is a great city to walk around and explore. The neighborhood to the east of the Nidelva River is particularly charming. There are two bridges: walk across the Old Town Bridge (Gamla Bybro), then walk north and cross back via Bakke Bru. But while you're over there, it's worth walking up to Kristiansten festning (the old fort). A lot of history there. I'd say after the cathedral it's the sight most worth seeing in Trondheim.
And of course explore the main downtown area and the waterfront. There's a lot of public art. There are a few museums, but I didn't visit any of them so I can't advise you on which are worth going to.