I hope it's not too rainy in July...We'll be on the Connie, July 16 sailing...and I want to enjoy visiting Copenhagen again...
Ine pretty much ran through Amsterdam for you...my only addition to Ine's list would be the Portuguese Synagogue...
As to Copenhagen, ...well, it's just a great town...aside from palaces (Tour the Rosenborg) and museums, my favorite things to do are to enjoy the city itself: Stroll up and down the Stroget (Copenhagen's main walking/shopping street--pedestrians only, great stores and places to get a bite to snack on...Have lunch-or a beer- in one of the outdoor cafes along the incredibly picturesque Nyhavn...Get a canal boat tour (you can pick one up at Gammel Stam)...Some folks love visiting Tivoli (world's first amusement park)...I don't...I found it crowded and disappointing--not worth the admission...but, if you like those sorts of places, okay...
Oslo was not my favorite port...We did a tour of the Vigelund Sculpture Park, the Ski Jump and the Open Air Museum (every one of the ship's tours seemed to include the sculpture park and ski jump in some combination)...Although all three sites were in some ways interesting, none were really that exciting...I also wandered the fortress which sat next to where the ship was docked...got some great photos from there...
I haven't been to Helsingor...
Have fun...