There are number of Beautiful places near Shimla as follows
Kufri Tara Devi Temple
Mashobra
Tattapani Naldehra
Thanedaar
Tani Jubbar lake Narkanda
Hatu Peak Fagu
You can go to Sadhupul it's a River side destination with a beautiful view. Camping is also available only for 800 per tent excluding food, also you can do a water fall trek which is 6/7 km from Sadhupul. If you like trekking den u should go to Shali tibba trek or Hattu Peak. Both are the highest peaks of Shimla.