Amsterdam, Copenhagen and Stockholm- 10 nights total

Honestly, that's going to be an intense itinerary. You have 10 nights; that's only 9 full, mostly-not-jetlagged days. You'll need to fly from Amsterdam to Copenhagen, which will probably cost you over 5 hours door to door. For me, dealing with airports is a major issue in the middle of a vacation. You'll barely have gotten to Europe before you're headed back out to Schipol.

Train time between Copenhagen and Stockholm exceeds 5 hours, to which you have to add the time spent traveling between hotels and train stations. In all cases there's also the bit about checking out of the old hotel and into the new one.

Now your 9 days have turned into 8, during which you have to get oriented to 3 different cities. These are not small places, nor are they short on sights. There's a risk you'll be running around like crazy people. It would be easier if you didn't care about art, but you said visiting art museums is a must.

My recommendation is that you postpone Copenhagen until a later trip. I gather you already have airline tickets into Amsterdam and out of Stockholm, that's why I'm suggesting Copenhagen is the one to omit. Unfortunately, you'll still be stuck with a mid-trip flight.

Divvying your time up between just two cities will give you some breathing room. You should then be able to see the Kroller-Muller Museum in Otterlo with its large collection of Van Goghs, and perhaps the Mauritshuis in Den Haag, as well as the major museums and other sights in Amsterdam.

I've recently made a return visit to Stockholm and have at hand my list of sightseeing targets. These are the art museums on my list:

• National Museum (the largest; also good decorative art)
• Millesgarden (outside the center; takes time to get there)
• Moderna Museet (special exhibitions usually contemporary)
• Magazine III (contemporary art, outside the center; I missed this one)
• Sven-Harrys Konstmuseum
• Hallwylska Museet (also decorative art)
• Liljevalchs (also decorative art; on Djurgarden)
• Waldemarsudde (also decorative art; on Djurgarden)
• Thielska Galleriet (on Djurgarden)
• Artipelag (contemporary art, way outside the center and expensive; check website to be sure it's of interest. I mainly enjoyed the outdoor sculpture park. It's a major time commitment to get there.)
• Fotografiska (large venue showing special, crowd-pleasing exhibitions of photography, on Sodermalm)

Not that you'd want to go to all those places, but those are just the art museums. Stockholm has a lot more.

If sticking with all 3 cities is a must, I cannot improve on the way you've distributed your time.

As for hotels, you'll get the best advice by telling us your nightly hotel budget and the key sights you want to see. With so little time, I think you need to choose very conveniently located hotels, but "convenient" depends on your sightseeing targets.

I think it is a busy but doable itinerary if you embrace the hustle of it. I’ve done a 3-city 10-day trip before and thought it wasn’t too much traveling.

I suggest taking evening flights (or train for Copenhagen to Stockholm) between your cities to maximize sightseeing during the day; most museums and sights are closed at night so you’re not missing anything there.

Copenhagen is great, I didn’t see all of the art galleries there but it is a fun city and if you’re not planning to return to Europe soon I think it is worth a stop.

I suggest eliminating one of your cities. 10 days is not enough for the three.

I have been to all 3 of the cities. Amsterdam, been there twice and the last time last year. We spent a week there. You need more than three days to see it all, especially if you do the Anne Frank House, the Rijksmuseum and the Van Gogh Museum.

Copenhagen, we have been there three times and love that city and Denmark. Again, you need 4 days to see the city and the nearby Viking Museum and some great castles.

Stockholm, don't miss the Vasa Museum, it is special.

Doable, but will be very rushed. You can however save a bit of time by taking the overnight train from Copenhagen to Stockholm. Otherwise, three nights means two days and you won't see much of neither Copenhagen nor Stockholm with that little time.

As you already have your flights, I'd drop Copenhagen. If these cities were closer together I'd have no problem with three in that time period, but not at this distance. As much as I don't encourage interEuropean flights, with your schedule, if dropping Copenhagen, it is likely your best option. Amsterdam and Stockholm are almost 900 miles apart. If you don't drop a city, then I would be excited about the overnight train from Copenhagen to Stockholm, which as Badger says, will give you one more day in a location.

Basically you have 3 days in Amsterdam, 2 days in Copenhagen, 2 days in Stockholm. That's OK for a light feel of each city, and if you spend a lot of that time in art museums, then you will get even less of a feel for the actual location. Not that that's bad, if that is how you travel, but just putting it out there.