Last year in Copenhagen we were prepared for high prices. Well... first, in our hotel, a huge breakfast buffet.

After that, lunches - we always managed to find something less expensive, like $30-40 for 2 people, if you are not picky. In addition, "ethnic" restaurants are cheaper.

To save, we got Chinese take-out or ready-to-eat and some veggies from shops to have dinner in the hotel room - our had a balcony overlooking the main square.

We live in San Francisco, so the restaurant prices in Copenhagen were not particularly shocking.

Another option you might want to consider is a cruise. (I know, I know, but we were never cruise people before we sailed the Baltic...) A Baltic Sea cruise is an excellent, inexpensive way to visit many of the top cities of Scandinavia (usually begins in Copenhagen with stops at Oslo, Helsinki, and Stockholm). Our Holland cruise also stopped at Tallinn and gave us 2 days in St. Petersburg. It's really quite a good value.

Another money saving tip: On days in port, we would eat a large breakfast on the ship, and then we often packed a lunch/snack (from the ship's buffet)and took that with us for later in the day.

I was a seaman. I used to have lunch in Stockholm, Helsinki, Copenhagen etc. Most I spent 8-12 euros for lunch. Even, there is one very popular restaurant in Stockholm named "Pong" just 100 meter from Stockholm train station. It costs you 8 euros for regular days. At weekend It costs you 12 euros. It's buffet. You can have as much food as you can including fruits. I believe the food is good not only for me, Asian, because I always saw a lot of white people (Maybe Swedish) having lunch here.

Also, many times, I had sandwiches in Oslo, Helsinki, Tallinn. It's not expensive.

Copenhagen prices are significantly cheaper IME than Sweden, Finland and especially Norway.

ScanRail Pass holders get discounts off hotels of some chains throughout Scandinavia I believe.

bookmarking

I sure wish that link I posted for hotels still worked.

We are heading back in March 2014 and the link is dead. :(