Booking.com is a convenient first stop since it has listings for so many hotels, as well as for some apartments. Scandinavia is expensive, and I ended up in a lot of chain hotels there when they turned out to be the least expensive, centrally located option. You don't usually need to worry about quality of lodging in that part of Europe; it's a matter of avoiding personal bankruptcy. Joining the affinity group and booking on the corporate website usually saved me at least 5%. This year, I'm seeing some larger discrepancies between booking.com rates and hotel-website rates (albeit in other parts of Europe), so you definitely should check both sources. But I've found both the ratings and the reviews on booking.com very helpful; you can't leave a review there if you haven't stayed in the property.
The chain hotels aren't usually charming, but they should have reliable plumbing and Wi-Fi, and in most cases they'll offer a good breakfast. There are some newer, low-service chains that don't offer breakfast at all, and in other cases breakfast is optional. In the second case, the breakfast charge will usually not be cheap, but if you are eaters of full breakfasts rather than part of the coffee-and-pastry brigade, indulging in a Scandinavian breakfast buffet, for at least some days, is part of the cultural experience.
You're unlikely to encounter a serious heatwave, but you might be a bit unhappy without air conditioning in July/August. Not all hotels will have it, so that's something to think about.
These are chains I used in Scandinavia and Finland. I have no idea which might have rooms to accommodate three people (or breakfast), but you can filter for that easily on booking.com. These chains will not necessarily have hotels in the cities where you're staying.
- CityBox (I think no breakfasts, and low-service)
- CityLiving (I think no breakfasts, and low-service)
- Scandic
- Comfort
- Best Western (these sometimes have local character and are often nicer than in the US; I've stayed in quite a few because the rates were good when I made my usually-late reservation.)
- Clarion Collection
- Elite Hotels
- Strawberry Hotels (new name for Nordic Choice--heaven knows why)
- Sokos
- Holiday Inn (also may be nicer than you'd expect)
I haven't stayed in a Thon Hotel, but they are often recommended here. I'm sure there are other good chains. What I'm not sure about is rooms to accommodate three people. It's possible the chains are less likely to have something other than a double or twin room. But again, booking.com will be helpful as a first step.
On a short trip to Stockholm, a convenient hotel location may matter. The other places you're staying will be a lot smaller. The Metro in Stockholm is very useful, so pay attention to hotel location vis-a-vis Metro station. I think Badger and I agree that the area immediately around Stockholm Central isn't the most interesting place to stay. However, it could be an efficient choice and less expensive than areas with more charm.
If you're not going to have another opportunity on this trip to see one of the best Norwegian fjords, I'd highly recommend taking the Norway-in-a-Nutshell route between Oslo and Bergen. That means breaking away from the mainline train route at Myrdal, then taking the Flamsbana train down to Flam, the Naeroyfjord ferry to Gudvangen and the public bus up to Voss before re-joining the train. That can all be done in one longish day, but you'd be well advised to get an early start (buy Oslo-Flam ticket well in advance from vy.no, paying with PayPal); the transfers are super-easy. If you should decide to spend a night or more along the way, my guess is that your best shot at finding a hotel room would be in Voss. Flam and neighboring Aurland book up really early. I ended up in a private room in the hostel in Flam (perfectly fine--like a low-end dormitory room), where there was little else available.
