I wouldn't plan to use taxis. They are likely to be shockingly expensive. But public transit is very good.
Frogner is distinctly uphill from the center of the city. I stayed at Coch's Pensonjat (and would heartily recommend it to other serious budget travelers), and most of the time I did the walk both downhill and back uphill at the end of the day. But the Frogner area may be even more uphill (I don't remember), and it's far from nearly all the traditional Oslo sights than I was except perhaps those in the Aker Brygge area. I took transit from my hotel to Frogner Park. I must have been in a hurry, because I know Rick has nice things to say about the area around Bogstadveien/Hegdehaugsveien/Majorstuen, and I missed that area.
Incidentally, if you're flying into Oslo, you can take one of the regular trains into town that stops at the Nationaltheatret Stasjon, which is a lot closer to Frogner than Oslo Sentralstasjon is. As of 2022 a ticket on that train allowed one to use public transit for the next hour or so, making it possible to hop on a bus or tram to cover most of the distance to a hotel. Of course, you can use that same feature if you take a regular train and get off at Oslo Sentralstasjon.
I think this decision (aside from potential financial aspects of it) comes down to how you prioritize traditional sightseeing and wandering around interesting neighborhoods. I very much enjoy both.