Back to city you could explore kalibari temple, visit Christ church stop by scandal point. Third day you could enroll for heritage walks or plan visit to fagu, solan and Kasauli.
You need minimum 3 days to visit Shimla. You could start with Jakhoo temple then visit Green valley come back to the city to explore visceral lodge, state museum and Rothney castle. Evening stop by lakkar bazaar try horse riding, step into cafe hide out and try some local cuisines. Next day you could plan travel to kufri which is 9km from Shimla. Stop by Himalayan bird park, Annadale, reserve forest and get back to the city or stay in kufri.