8 Day Trip to Norway Mid August - Looking for suggestions for must see places

Going around the same time.
It is a hard question since we don't really know your interests and what you want to see also it seems most tourists do the NIN routes and don't venture to some lesser publicized areas.

It is also a large country, not wide but tall and many times you cannot drive what would be a straight route to get places and need ferries as well.
For this reason I suggest visiting a website like VisitNorway.com looking at the different options ; that is an excellent website. Spend a good amount of time on the site, selecting a handful of spots that really catch your eye and then pinning them on a map to see how far away different places are, what is feasible.
After you determine a main spot to go, look for smaller sites not too far off and you can make a day out of it.

I have only been to Oslo before and while a nice, pretty and very clean city it didn't have much that wowed me as a tourist, since not sure it is a must on a Norway itinerary personally. If I want a city vacation in Europe it would always be better to go to Amsterdam, Paris, Rome, Florence, London, etc...
I am sure opinions will differ though.

Figured I would share how I came about my plans which may help you.
Originally I had planned on flying into and out of Bergen ; while I found quite a few places to drive to from Bergen the #1 spot for us was Geiranger and it's fjord ; in my top 5 were also nearby Romsadalen Ridge and Trollstigen. I realized all 3 of these places were too far a drive from Bergen though so ended up changing my plans to fly into and out of Alesund which is much closer to all 3 areas.
It of course meant Bergen and all of the cool waterfall and hiking spots around Bergen as well as Stave Churches and other fjords had to now go as well.

So my plan is now limited to a fairly small area where there are a couple of fjords, Geiranger being the main one and the mountains I was looking for. For our 5 nights it made sense and the smaller city of Aselund will be our only taste of the city.
Not saying to change your flight or lodging just to identify how far you can travel and what interests you the most:
Fjords, hiking, waterfalls, city walks, walk on a glacier, boat rides, train rides, stave churches, etc...

Given that you are posting on the RS forum, starting point would be RS points of interest:

https://www.ricksteves.com/europe/norway/oslo
I would spend two full days touring Oslo's sites.

https://www.ricksteves.com/europe/norway/fjords
NIN tour

https://www.ricksteves.com/europe/norway/bergen
As part of NIN tour.

National Parks:
https://www.visitnorway.com/places-to-go/eastern-norway/the-jotunheimen-mountains/
Jotunheimen National Park: Walking the home of the giants.

One of the highlights is the path along the narrow Besseggen ridge
from Memurubu lodge to Gjendesheim lodge. The view southwards over an
emerald coloured Gjendevatnet lake (3,228 ft. above sea level) and
northwards over Bessvatnet lake (4,504 ft. above sea level) is a real
treat.

https://www.visitnorway.com/places-to-go/eastern-norway/rondane-national-park/
Rondane National Park: Norway's first national park.
http://www.discover-norway.no/rondane-with-luggagetransport

By Norwegians, the Rondane massif is one of the most beloved hiking
areas in the country. Rondane National Park is an ideal place to
experience the mountains and highlands of Eastern Norway. This was the
first National Park in Norway, listed in 1962. Today, it covers an
area of almost 1,000 square kilometres.

Within the Park you find ten peaks that reach beyond 2,000 meters in
height. Not all of them are reachable on this tour, but from Mysuseter
you can hike some. The fittest actually make six summits in one day.
At Høvringen you are in the highlands, where the mountains are easier
to climb, and the landscape calls for peace and meditation. From the
mountain Formokampen you have great view of the Rondane massif, and
from there you can proudly point out the places you've been.

True Edgar, but Rick's advise is limited to a small section of Norway. He has not covered from what I have seen most of the country so in this case I am not sure is the best resource.
I think the forum is allowed to give advise outside of the guide books, tv shows, etc... which are excellent but for some countries provide limited information.

MR: Rick's advise is limited to a small section of Norway.

True, but I did note that the RS advice is a "starting point" and added my suggestions (of places I would visit). It would help if we know what the OP is interested in seeing/doing. I personally think of Norway of an outdoor adventure playground. If museums are more to the OPs liking, I would add the Folk Museum in Lillihammer: https://www.visitnorway.com/listings/maihaugen-museum/5314/
The outdoor part of the folk museum wasn't open when we visit but the inside museum time tunnel was interesting:

...like the indoor exhibition "We won the land" where you walk through
tableaus from Norwegian history from the ice age till today.

In terms of just driving around, OP may be interested in stave churches (see map):
https://www.visitnorway.com/about/history-traditions/stave-churches/

I see those additional links, my bad I mis-read your original post. No offense intended.
Yes, depending on the OP's interests I imagine there are more options they can fit into their number of days.

We are just finishing 11 full days in Norway. As others have suggested, knowing your own interests and using RS and other books as a guide you can pick and choose from the opportunities. Our own example follows. We wanted several full days in Oslo to see the sights there, some time in Bergen and then a good exposure to the fjord and mountain country. After looking at NIN and other tours, we decided to rent a car in Oslo and then drive to Bergen and on through fjords and mountains by weaving together a path along 7 or 8 of the National Tourist Routes. That combo gave us the exposure to both urban and rural scenic Norway we wanted. The time in the cities was excellent for history and culture, the rural time was a great overview of the truly amazing sights in the fjords and mountains. I will be posting a more detailed trip report in a couple of weeks. For now I'd suggest you take whichever guidebook you like best, list the opportunities therein on a prioritized list, calculate how much time each one takes and then draw a line when you reach 8 days. If this is your first trip to Norway you can hardly go wrong. Have a fantastic time.

Oh, I'm jealous! I spent 11 nights in Norway in 2014. I'd second the folk museum in Lillehammer, especially if you're staying there. If you want to drive north a bit, you could see Innerdalen, which I didn't know about when I went but won't skip when I go again. You could also drive the Trollstigen Road which has some of the most gorgeous driving routes to the north and south of it. Trollveggen is right there, too; unfortunately it was so cloudy when I drove through that I couldn't see the famous peaks! Oslo is a lovely city but I think the grand beauty of nature is where Norway really shines so when I go again I won't spend much time there. I only spent two nights (1 full day) in Bergen and 3 nights would've been better. I also would've loved to have spent more time in fjord country. One night in Solvorn wasn't nearly enough; 3 would've been great.

Have a wonderful time!

We are currently in Oslo after driving/seeing much of Norway between Bergen and Molde. Here is my suggestion. Drive from Lillehamer to Lom. Visit Lom Stave Church. Continue on road 15. Consider staying at the Elveseter Hotel (if they have openings at this late date). If they don't have openings, stop and wander through the main part of the hotel in the reception area. It is spectacular and authentically Norwegian (FYI...Elveseter rooms are basic and clean.). The included breakfast buffet is wonderful. Continue on National Tourist Route 55 through the Jotunheimen National Park (and I hope it is not raining like crazy as it was when we went through as we could see that it is spectacular). BTW, this route is recommended in Rick's books and we followed his guidance for stops. In addition, we toured the Kaupanger Stave Church which is prior to the Kaupanger/Laerdal ferry. (BTW, no ferry reservations needed...and don't be shy about taking ferries. Fact of life in Norway.) If time, visit the Urnes Stave Church OR drive the National Tourist Route "snow road," stopping at Stegastein Overlook (all mentioned by Rick). Stay the night in Aurland (AirBnB is a good resource for places). Take the Flam rail ride as planned (get tickets in advance!). Head to Bergen after this. We did almost everything recommended by Rick in Bergen. Luckily, we had spectacular weather. Two of the 60 sunny days they get in a year!