Shimla is beautiful hill Station of Himachal Pradesh. You can explore number of Tourist spots before reaching Shimla on the way to Shimla from Chandigarh like Kasauli Barog Dagshai Jail Solan Shoghi Tara Devi temple
After crossing Shimla You can go to Kufri Mashobra Naldehra Fagu Narkanda Hatu Peak Thanedar Tani Jubbar Lake
Amritsar is another route you could try. Shimla is 7 hours away from Amritsar.,On the way you could stop by Gobind sagar lake, rose garden, then enter Chandigarh stop by Rick gardens , Sukhna lake. From this lake Shimla is 3 hours away. Some spots you could touch before reaching Shimla is Chail 1 hour away from Shimla
Narkanda is 2 hours away while Shoja is 5 hours away.