I'm traveling to salzburg on the 14th october and will reach there in the afternoon. Planning to stay there till the 17th of October morning from where I fly to mallorca. I plan to explore around Salzburg on 14th. On 15th I plan to go to Berchtesgaden, kings lake and eagles nest by public transportation and return back to Salzburg in the evening. On 16th I plan to go to hallstatt village, dechstein ice caves and 5 fingers (or schafberg rail ride or werfen ice caves instead depending on transport availability and which are closer) again by public transportation and return back to Salzburg in the evening.
In Salzburg, please suggest on the places that can be visited.
Please let me know if traveling to these places by public transportation is a good idea and if it would be economical compared to renting a car. We are two people and had got a quote for renting a car from Salzburg airport for 120 euros for 2 days with zero excess and with a deposit of 150 euros (renting using a debit card using a company called indigo car hire based out of UK). I'm skeptical of driving around in Austria (as it would be my first time driving in Europe). I have my Indian license in English and dont have a IDP (rental company said it's not needed).
Also, please feel free to suggest any alternative places to visit if they are more beautiful and easier to access than the places I have written above or also if I should cut down on the number of places to be visited.