Day trips from Salzburg

Berchtesgaden is just south of Salzburg and an easy trip.

Weather would be a deciding factor for you to go or stay in Salzburg. There is bus transportation to the Königsse. Sorry but I cannot give you the details. I recommend the electric boat on Königsse to the Obersee. Hike to the Fischunkelalm. The hike has some rough places. Wear good shoes. Be prepared for a rain shower. The Alm will probably not be open this early (no cows either). Do it anyhow. I've been there in early May. On a beautifully blue sky day the view from the Fischunkelalm back towards the Königsse is stunning. You won't forget it. Quiet too. It would be a long day.

See my post about my day trip to the Wolfgangsee

Let's guess that you will purchase a Salzburg pass. This will allow you a free ride on city transport as well as the Untersburgbahn.
https://www.untersbergbahn.at/
Another great getaway to nature that will cost you nothing as part of the Salzburg Pass is taking Bus 151 to the Gaisbergspitze. More fantastic views as well as a spot for lunch or snack at Kohlmayr's.

Thank you everyone. This is really helpful. We are planning to visit Berchtesgaden and Konigsee. I was trying to book the bus 840 for 7th May from OBB website, however it says "Ticket not available". Does this mean its only available to buy in-person or that all tickets are sold out already? Are there any other websites I should check?

Bus #840 is a joint venture between a subsidiary of DB and a Salzburg bus company. It is possible that ÖBB only shows the timetable but does not sell tickets. Simply buy your ticket from the bus driver (platform J).

When I took the bus from Salzburg to St Gilgen, it started from the train station so naturally I assumed they would have a ticket office inside. Nope. The guy at the info desk said just buy your ticket from the bus driver, which is what I did. I think if I had more time I could have used a ticket machine at the bus stop as well.

Coming back I owed some money on my ticket and again I paid the driver.

Also FWIW

https://www.bigboytravel.com/germany/berchtesgaden/gettingtoberchtesgaden/

I'm a bit baffled by the concept of a "half day" trip to Hallstatt. It's 3 hours round trip. Sure it's a pretty drive through the mountains, but why spend 3 hours in a bus with maybe only 1 or 2 hours in Hallstatt? Download the same pics throngs of tourists take every day and enjoy the area around Salzburg. You've already mentioned enough to fill more than 3 days. Both Berchtesgaden and Konigsee are on the bus route. You don't need advance bus tickets.

Konigsee boat ride to the old church
Jennerbahn gondola ride
Salt mine
Nazi sites

If I remember correctly, the #840 bus is a German bus serving that area of Austria, and B'gaden is in Germany, thus you pay the driver directly. It's just like a city bus. You can catch it at stops outside the old town. It makes for a very beautiful day trip. ( There's also the salt mines, along the way.) Email the local TI, they should have the schedule.
You buy bus tickets for Austrian buses, that's the difference. The #840 is a German bus.
Enjoy!

Thank you so much for your helpful tips. Its such a relief to know bus tickets can be bought on the bus, I really thought I have missed the bus (pun intended)!