A small cantonment area 5-6kms uphill from Mussorie is definitely worth spending a day if you are in Uttarakhand.
You can take a cab \ bike or even hike from Mussorie to Landour.
Things to do in Landour
1. Enjoy walking ~3-4kms upper chakkar loop.
2. Buy peanut butter & jams from Anil Prakash’s store
3. Try pancakes at the oldest shop in Landour – Char Dukan
4. Relish delicacies at Landour Bake House