A friend and I will be in Scandinavia for a week. Our home base is with a friend who lives in Stockholm. We would like to make the most of our short time there, any suggestions on the quickest, most efficient, as well as cheapest, where possible, way, and places to go, so that we can see as much as possible during our stay?
We'll need some more details. Like where do you plan to travel? One week is barely enough time to see Stockholm and maybe one other city. I suggest either taking the ferry to Helsinki for the day and/or adding Tallinn too. Another option is Copenhagen but you'll probably want to fly as its a 5-6 hour train ride. Do you have your international flight arranged yet? Perhaps an open jaw ticket to Stockholm and from Copenhagen would work.
From Stockholm a ferry to Helsinki is worthwhile, maybe a triangle route adding Talinn. Another side trip from Stockholm I would want to consider is Uppsala. It's very historic and a college town not far from Stockholm. I don't think you will have time for much more in a week. You will also want to see the sights in Stockholm.