Sweden: Stockholm & Umea
By classic, you mean no too modern? most restaurants in sweden tend not to have a classic atmosphere. In general, they seem quite modern to me. Sweden is quite pricey btw.
It's probably better if you check the websites and see if you like the interior.
Viktoria (above) is said to have the best food out of those three.
For Stockholm I'm not sure what to recommend. I've dined there many times but your request is a little vague. What kind of food, price level etc? Does it have to be a la carte or are degustation menu places of interest? Are you more into the bar-like places with cool vibes etc?
Stockholm has a lot of korvkiosks (hot-dog stands) but I don't know anyone who eats there regularly. They serve whatever passes for hot dogs there along with assorted condiments (some familiar, some a little odd) as well as other hotdog stand fare. Many of these are also kebab stands (is there a city that doesn't have kebab stands/stalls?) Th other ubiquitous sandwich is the open-faced mound of mayonnaise-soaked tiny shrimp that are all over the place (even 7-11 (and, IIRC McDonald's) - which are much cooler than in the US).
Swedes also have an affinity for Thai food, so you'll find many more than you'd typically see in Europe.
In the European tradition Stockholm has a large foodhall in Ostermalm. It's primarily full of stalls with various foodmongers (meat, fish,cheese, bread) where you can shop for ingredients for the evening's (or day's) meal. It also has a number of prepared food stalls on its perimeter, offering sushi, Lebanese and other dishes (I had an excellent falafel sandwich there).
Gamla stan, the "old city" section has more fast food options than I'd like to see, but you can get a good cup of coffee and sweets in various shops (I don't recall a single name, but if you wander around, some will stand out).
Oh, and nothing's "cheap."