Oslo transportation logistics

Either way works. If the weather is nice, you can walk. Takes 15-20 min or so and has some nice views of the fjord. Or you can take bus (stops just outside the terminal) to the central station and from there the metro to Stortinget.

Best source for local bus is Eurail website. Eurail pass doesn't cover local buses https://community.eurail.com/eurail-interrail-passes-41/does-eurail-pass-include-local-trains-within-certain-cities-for-example-rome-2622

Buy an OSLO PASS - we bought ours at the TI at Centraal station, downtown Oslo. free bus & trams, free or reduced museum admissions, free ferry for trip to Bygdoy island.

Oslo is one of the most walkable cities. Lots happening along the waterfront and along your walk route. Nobel Peace Center. Oslo City Hall (Radhus) with spectacular murals;
walking to Opera House roof fyord-side; take ferry to Bygdøy museums (several museums on the island - 100% intact Viking ship; Kon Tiki museum, stave church; Maritime Museum, Fram and a recreated 1800's village; delish cafe; pleasant walking between museums.

https://www.visitnordic.com/en/article/public-transport-in-oslo get RUTER transport app.

The Viking Ship Museum is closed for major work. There are some Viking displays at the Historisk Museum not too far from your hotel.

A lot of guidebooks haven't been updated yet to include the new MUNCH Museum on the waterfront, in the same general area as the Opera House, or the new National Museum farther west.

Both sell time-slot tickets. I found no need to buy early in mid-June, but I can't guarantee that's always the case.

Oslo is full of amazing world class sights.
Here’s a list of them:
Fran Museum of the polar expeditions in the early 20th century
Kon-Tiki Museum right next door to the Fram, both can be reached by ferry
Frogner Park with the massive sculptures by Gustav Vigeland, we reached this by our tour bus so I don’t know how you would get there. Where is your hotel, what part of town? The park itself is gorgeously landscaped with hundreds of acres, lakes and birds, etc.
Oslo Opera House has a ramp like rooftop that invites you to walk to the top for wonderful views of the waterfront. This requires you to be somewhat fit as it’s a climb. If you are interested in the behind the scenes of the production, there are tours you can sign up for online.
Munch Museum right next door to the Opera House is amazing and the cafe has gourmet food. We had lunch there and were blown away.

I see your hotel is fairly close to the center of town and it appears you are in walking distance from the waterfront. As the poster above said, Oslo is a very walkable city.

Depending on your available time in Oslo, you will not be bored.

We had a wonderful experience staying at the Grand Hotel, excellent, helpful concierge. Concierge sent us to the tourist office nearby, told us what transportation pass to buy, mapped out our whole time in Oslo. We easily walked or took public transportation all over the city. Look forward to returning.

You can buy bus or tram tickets at any small convenience stores - they're called Narvesen. I don't think Rick's Scandinavia book is clear enough about this very critical piece of info.

Narvesen. That's where you get tram/bus tickets. And the main train station is called "Oslo S" on the self service train ticket machines.

Rick's book wasn't clear about that either, which is a major problem when you have a late arriving flight and there's not much airport staff left to help you. Ask me how I know (grrrr). Yeah I was cursing Rick Steves for some major overlooked info in his books.

Also download the CityMapper app to use public transit in any major world city. It'll help you navigate any world city including Oslo.

Some locations of some other convenience stores (Deli De Luca, 7-11?) also sell transit tickets. I'm nearly certain Rick has that info in his book. I'm not sure every branch of the participating chains sells them.

However, you should be sure whether you're buying a ticket for immediate use or one you xan carry around in your wallet as an insurance policy. I know I ran into a problem doing that somewhere, though I don't think it was in Oslo.

We just left Oslo. We purchased a 24-hour transportation pass that let us ride trams, buses, etc. However, we never ever saw anyone using a pass and never ever saw anyone checking for passes. Maybe they do that randomly?

There are random tickets checks, and big fines if you are caught travelling without a ticket.

What Badger says abut ticket inspections:
https://ruter.no/en/getting-help/ticket-inspections/:

Read FAQ about ticket activation/validation.

We were oce on a tram stopped for ticket inspections. Transit police came in the front door and stationed police at the back door to catch ticket scpfflaws trying to escape inspection.