kunsthistorisches museum

The KHM does not offer or require timed entry. Others, such as the Upper/Lower Belvedre require it. You need to check each museum for their respective ticketing processes.

I tend to travel during the shoulder seasons, so I don't normally run into issues with getting in to any museums. I expect that June is busier. What I do is plan my day at breakfast and book a time slot or open entry for a museum I wish to visit. I do this online on the museum's website. Tickets are often discounted and I skip the ticket purchase line.

I was in Vienna last June. Loved the city. Because I was there for a week, I bought two annual museum passes. It was cheaper admission for the museums I wanted to visit. For a shorter visit the passes may not be worth the money. Tickets at the door and no waits seemed common.
https://www.schoenbrunn.at/en/all-tickets/sisi-ticket
https://shop.khm.at/en/tickets/detail?shop%5BshowItem%5D=200000000009138-T054-01

The only venue you need to prebook is the Spanish Riding School (Lippizan horses). The performances and especially preferred seats fill up. https://www.srs.at/en/
I also prebooked seats at the Vienna Opera. https://kalender.wiener-staatsoper.at/en/calendar/2024/june/

Enjoy your visit!

@ jkh and Horsewoofie - thank you for your replies! I'll look into the museum pass and see if it's a good deal for 3 days.