Mussoorie is around 35 km from DehraDun. This is also called the queen of hills. It is a beautiful small city which is famous for GunHill (which can be reached by rope way from Mussoorie), Company Garden. There is also a very famous IAS Academy at Mussoorie. The famous Kempty fall is very close to Mussoorie. There is also famous places like Dhanaulti nearby.
You can check https://ChatpataDun.com There are lot of trekking options also available around Mussoorie.