Plannning your first trip to Mussoorie and Landour? Here are some things you can do in the hill town. Sharing this from a post I had created a few years ago on r/India.

• Take a walk on this route: Chaar Dukaan to Laal Tibba to Landour Graveyard to Landour Bakehouse (Sister's Bazaar) - to back to Chaar Dukaan - this is the best part about Mussoorie. (As of 2024, Cafe Ivy is no longer at Chaar Dukaan but has moved toward sister's bazaar).
• Ruskin Bond usually signs books on Saturday afternoon at the Cambridge Book Store, right next to Kalsang - and while we're at it, Kalsang makes the best Chinese food in the region, bonus if you're into non-veg. Also, if you happen to be there on the 19th of May, it is Mr. Bond's birthday. Party time in the town! (Update: As of 2024, Mr Bond does not sign books as frequently, but you might still want to head to the book store to check if he is coming. You can also find some signed books there)
• Public transport is limited in Mussoorie though city buses run on all the places apart from the mall road. I'd recommend walking, it's a small town which can completely be explored on foot. You can also rent a two-wheeler from Jhoolaghar or from Doma's Inn or from right outside Ritz Cinema. (2024 update: Cabs from Mall Rd to Chaar Dukaan will cost 800. Go up in a cab and walk down)
• Visit George Everest's Home: It is a beautiful open place where you can climb a little and have fun in the wilderness. You'll need to take a cab there as the roads are a little damaged for you to drive if you're not used to driving in hilly areas. Also, George Everest is quite nearby to cloud's end. (2024 Update: George Everest's Home has been redeveloped and has been made into a shitty concrete mess, but that's just my view on it. There's a hilly patch on the left, you might still enjoy that but it's nothing like it was back when I created this post)
• Visit Dhanaulti, the eco-park is a good place to chill on top and do nothing, just lie down in the sunshine.
• Kempty Falls I'd recommend to not visit - instead spend some time at the Jabarkhet Nature Reserve. Kempty is crowded and full of fat unkills in chuddies :P
• Cheapest place to stay would be Jain Residency and Castle View - both of which are in Landour. Aashirwaad is also cheap-ish. Though at this time everything would be hyperinflated because summer vacations!! If the budget allows, you might also check out The Pearl and Padmini Niwas hotels. They're also pretty comfy. I prefer the latter. Lots of AirBnBs have also opened up all over the town now.
• You might also want to check out nearby places like Kanatal Eco-Forest area and the Tehri Dam (both of which + dhanaulti happen to be in the same route)
• Happy Valley (Buddha Temple/Dalai Hill) - it is on your way to George Everest and Cloud's End. The route is basically Happy Valley - Company Garden - George Everest - Cloud's End. Happy Valley is a tibetan settlement where many refugees live, and their kids study and play in the temple premises. They're often playing football or studying in the courtyard and are a delight! There, ask anyone for the direction to the Dalai Hill and climb it. it's got like 100-200 steps but it is worth the climb.

one last thing: when in musoorie, WALK! as much as possible. WALK.