Scandinavian 10 day trip

I'm looking to plan a 10 day trip between Denmark, Sweden, and Norway. I've done a little bit of research so far and I'm looking at doing the three capital cities, with Bergen as an option as well. I'm going with a friend and looking to budget about 3k USD apiece. We're very early in the planning stages. We'll both be 21m by the time of our trip we're interested in nature, museums, food. We'll be flying out of Michigan US beginning to mid August. Looking for general advice/planning tips, this will be both our first time planning something quite this large, and so anything is helpful. Does this sound feasible and fun?