'Tur' is more for a walk, journey, visit, travel, etc. If you want to talk about a band or an artist going on tour the word 'turné' would be more appropriate.
For "A guided tour of/in Nidarosdomen" I'd say 'tur' would be an appropriate translation. ("En guidet tur av/i Nidarosdomen" would sound good in daily speach.)
The preferred translation for this sentence is "Do you like to go walking?".
Your suggestion, "Would you like to go for a walk?" has a different meaning than the Norwegian sentence, which asks whether you enjoy going for walks rather than whether you want to take a walk.
In Norwegian we can say both "gå på tur" and "gå på haik", which both refers to going for some kind of walk. Normally "en hike" is mostly referred to as a longer walk (preferably in the forest, mountains, etc.), and "en tur" is more casual (like walking to the store or maybe just for a few hours). So in short, both are accepted (but I think “tur” is a more common word to use?) :)