I'm from Trondheim, but I'd be of little help as I am away for now, and will be swamped in moving and furniture shopping when I'm finally back :I
Trondheim is a very tourist friendly city if you are a wealthy German, in that it has a small centre and thus quite easy to navigate, and it has all the usual comforts a German would be used to, like expensive coffee bars and other expensive shopping. If you want beer, you'd be better off with good old Prague, our beer is probably
the most expensive in the world, and as such, the most expensive in the entire universe.
Like Mutantscalper says, if you like hiking you can exit the city by virtually any direction in 10-20 minutes by car/bus. If you like to hang out with other Germans, go to Bakklandet, which our only real "tourist area"
Here you can enjoy tiny, brightly colored wooden houses and expensive coffee, and you can probably find places to eat actual "traditional food", like salmon or cod or herring, expensively of course - that goes without saying!
If you like to just stand and gawk at stuff, you can always go to the Nidaros cathedral, which is visible from anywhere
(gawking is free, so I recommend it!)
Or you can hang out at the Fortress park
it's also visible from anywhere in the centre. From the Fortress we stopped an army of 10 000 unwashed SWEDES from invading our proud Fatherland, we kept them at bay, with muskets and cannon fire, and they DIED LIKE MAGGOTS of dysentery in the THOUSANDS untill the final 6000 or so had to retreat across the mountains, BACK to Sweden. Only a couple of hundred made it, since they all FROZE TO DEATH in the NORWEGIAN FREEZING COLD!
https://en.wikipedia.org/wiki/Carolean_Death_March
If you go there, remember to stretch your clenched fists towards the sky, and bellow out a great victorious cry, it is customary! Also, this park has a lot of stoners, look around for any, if you wanna score some weed.
If you want vikingy stuff, there's two options - both are sort of tricky to find -
one is the science museum, the easyest way is to find the "Leutenhaven" garage, and simply circle around it, untill you spot:
which is not the main entrance, but used to be - either way, you should find the entrance easily enough once you spotted the building.
The other is an outdoors, open air museum, around the castle ruins of Sverresborg. I guess a taxi would be the best way to get there, but - it's gonna cost ya!
I'm a bit of a heremit, so these are the most obvious of attractions, I guess if you absolutely want to, you can go to the TV/Radio tower, which has a rotating restaurant, where you can eat really expensive dinner, while experiencing nauseating vertigo - AND spinning around, to make you nice and dizzy.
Also visible from anywhere.