Pune la bhet🙏

Namaskar mandali! I'm planning to visit pune with my mother from Mumbai. I saw an itinerary online which I'm thinking to follow. Day 1: •Pataleshwar mandir •Shaniwar wada •Lal mahal •Dagdusheth halwai ganapati •Raja dinkar Kelkar museum •Okayama friendship garden Day 2: •Aga khan palace •Tulsi baug •Parvati hill Few doubts of mine 1. I would like to cover more temples as well which should be given a visit 2. let me know if there are any other places I must visit 3. good budget friendly restaurants to have meals at. 4. are the above mentioned places well connected via public transport like bus/metro? 5. Good lodging with a budget of 1k per night