If your credit card doesn't have a chip, many places will not accept it. But as someone else said, make sure the credit companies know you are going overseas BEFORE you go. If you stay mostly in cities you probably won't need much cash, and I would just get it out of an ATM instead of carrying around a ton of it.
Depending on your cell phone plan, you can buy international usage but it is very, very expensive. Assuming you have a smart phone, just rely on WiFi hotspots. Text using WhatsApp or something similar.
Personally I like Stockholm and Copenhagen is great too. You won't have time on this trip, but if you ever go back to Northern Europe, check out Tallinn, Estonia. One of my favorite places that I've ever been.