~8 days in late September: Norway? Portugal? Switzerland?

All these places are great and I have visited them all more than once.

Regarding COST they rate as follows:
1) Portugal (cheapest)
2) Switzerland
3) Norway, most expensive country in Europe and I have been to almost all the countries in Europe.

As far as history, museums, castles, archaeological sites, Portugal would have the edge. However, Norway and Switzerland are two of the most scenic places in Europe.

The Norwegian fjords are amazing. Take a cruise that includes several Norwegian ports and you will maximize the scenic part of your visit to that country. Oslo is interesting, but not as scenic as the North Sea coast.
Here is my review of our six port cruise up to the North Cape of Norway in 2019. https://www.cruisecritic.com/memberreviews/memberreview.cfm?EntryID=659526&et_cid=3214772&et_rid=17221689&et_referrer=Boards

Switzerland is loaded with great Alpine scenery. Best place to start would be in Interlakken, close to the center of the country. If you like snowy mountains, you can ski in the Summer at Young Frau.

Portugal is also very scenic, but it also has history and castles. The most scenic part of the country is the Douro River Valley in the north. Porto is great, spend a couple of days there and either go up the valley by train to Regua and Pinhao or better, take river cruise for a week. Wonderful scenery with vineyards everywhere.
Here is my detailed review of our Portugal visit in 2016 that included Lisbon, Sintra (Castle), Obidos (town with ancient walls built by the Romans).
http://www.cruisecritic.com/memberreviews/memberreview.cfm?EntryID=535267

I’ve been watching a lot of YouTube videos of Portugal and I find it fascinating, it’s definitely going to be one of my top choices for my next trip.

So, I’d suggest spending a few hours watching YouTube videos of each and seeing which one moves you the most. I love the walking around videos which take you through a city.

If it were me I'd pick a place I'd never been before.

Thanks for this! You're definitely focusing my thoughts. I haven't been to either Norway or Portugal, but Portugal is probably most different from places I've been recently-ish, and yes, Switzerland would technically be a repeat. I was aware that Norway could be expensive, but geovagriffith, you're making me think I should be saving it for more perfect weather than I'll get in late September, to justify the expense. (My job makes it tricky to travel in June/July, but I'm sure I could do it sometime.) I'm ordering the Portugal book now!

My last international trip was to Portugal and I highly recommend it! We spent time in both Porto and Lisbon, as well as 5 days driving between the two.

A favorite town was Guimaraes, not mentioned by RS, but with nearby Celtic village ruins, a beautiful castle, and a lovely former monastery Pousada on the hills above town we loved it. Coimbra was another special place, with students wondering the streets in capes and scarves, Roman ruins, great museums and food.

And everywhere, the most friendly people of any country I’ve visited.

Because you mentioned covid cautions: Portugal is going to provide more opportunity for outdoor dining. I just took my first post-covid trip (before test-to-return ended), and eating outside really helped me feel better. I also went with a direct flight (Madrid), and the way travel is going this summer, the easier the better--hopefully by September things will be calmer.

Our March trip to Portugal was amazing. I loved the country. Tons to do in the cities, easy transit between them, great food and wonderful people. Plus, it was about 30-40% cheaper than most EU countries we have previously visited. We will go back for sure.

I'm just going to throw in a pitch for Budapest, based on your criteria. The Hungarian history museum is the best I've ever seen of a bunch of national history museums, there is a really big castle right in the city, and there is a fantastic Roman city accessible by transit from the centre. It's also got great food, great cafes, and legendary night life. It would be quite easy to combine that with a few days in Vienna, which I also highly recommend for history buffs. You could spend a whole day (I did) in the military history museum alone.

Norway may be the most expensive, but if you're willing to leave from JFK in late Sept, there are fares under 250 USD with Delta (not a typo).

I'm going to throw in for Portugal here as well. I visited for the first time in may although with the exception of 1 day in Lisbon it wasn't much of a sightseeing trip, was able to return less than 2 weeks later for 8 nights with my husband - we split our time between Lisbon and the Algarve. We rented a car for the latter portion but in the end we didn't really use it much. We had no issue going from Faro to Lisbon by train, for example. And Uber and taxis are crazy cheap in the whole country, and quite available in our experience (less so if you were to visit more remote areas, surely).

Both trips made me wish I'd visited Portugal a lot sooner. I'm head-over-heels in love with Lisbon. And from everything I've read, late September is a wonderful time to visit. Because it gets quite warm, everything is well situated for for outdoor dining, and there's a ton of day trips you can do from a base in Lisbon that I didn't have time to do (I'd give at least 3 days to the city proper - it's big and there's a lot to experience). The food was amazing and very reasonably priced for western Europe. Lodging was a little higher than I'd like for a place as otherwise as inexpensive but still fine in the context of western Europe and a LOT cheaper than Switzerland or Norway. I stayed at a lovely AirBnB studio that was in an amazingly convenient and nice location with a full kitchen - please message me if you'd like that information.

Of the three, I'd go with Portugal. Both Norway and Switzerland are best explored mid-summer. Norway because it's north and September is a wet month. Switzerland because it's mountainous; weather is never perfectly reliable but it's most reliable in July to early September at the latest.