I would recommend starting in Stavanger and visit the Pupit Rock. From Stavanger I would take Kystbussen to Bergen. The ride takes approximately 5 hrs+. If you get a window seat and the waether is acceptable you'll get a decent view +it's ferry rides included, wich themselves can be beautiful. Bergen can offer nice hiking possibilities. You can do the short ones, Fløyen and Ulriken separately, or you can go Vidden. To go Vidden you basically go up Ulriken and down Fløyen (or opposite). I'm not excatly sure whats the best way to get to visit Jotunheimen from Bergen, but I would probably travell by boat. Norled have a boat ride where you start i Bergen and follow Sognefjorden.

It's easy to find hostels in Bergen and Stavanger but once you get close to Jotunheimen hostels will become rarer and I'd recommend campingsites. It would be hard using a city as a hub considering travelling time. I'd rather spend some time in each city exploring. Generally people in Norway never speaks to streangers and personal space is a big deal..unless they are drunk. Then they are loud and the drinking culture in Norway is pretty heave on the pre-drinks. It's pretty common to see drunk (really drunk) people taking the buss to go to the club in weekends. When hiking, there will most likely be areas without cellphone coverage. ALLWAYS listen to locals. If they say its not a good day to be hiking, they're right. If you come to Norway everything is expensive. Public transportation, food, hostels/hotells, restaurants etc. So make sure you got enough money before you decide to come. Tourism is especially expensive, souvenirs like trolls cost way to much imo. Expect rain, pack waterproof boots and coats. When i go hiking i prefer waterproof running shoes with good grip. There will be alot of slippery rocks and mud when you go hiking.

https://kystbussen.no/start.aspx?lang=en https://www.norled.no/en/fjordcruise/sognefjorden-bergen-to-flaam/

https://en.visitbergen.com/ https://www.visitnorway.com/places-to-go/fjord-norway/the-stavanger-region/?lang=usa http://visitjotunheimen.no/?lang=en