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.