I have seven days to work with, need help with my itinerary...

Seven days divided among three cities isn't a terrible idea if the cities are close together, but travel times will eat into a lot of your itinerary, so I think you are best off limiting yourself to two cities. I'd pick Stockholm and Copenhagen, but any two would probably be fine. It all depends on what you are interested in seeing and doing.

You need to do some research, as well as determine what kind of trip you want to have.

Do you want to see more places with less time in each place (a "tasting platter" kind of trip) or do you want to get to know each place in more depth, but see fewer places?

Do you want to focus only on the big capital cities, or spend time in other cities and towns, or see rural areas too?

As a related question, are there any specific destinations in these countries besides the capital cities that draw you? For instance, you certainly can spend 4-5 days in Sweden outside Stockholm - but will it be more interesting to you than moving on to another city/country?

It will take 1/2 to 3/4 of a day each time you go between your city pairs (such as Copenhagen to Stockholm). Sure, the flights are short, but there's getting to and from each airport, as well as waiting time. (Stockholm to Helsinki can be an overnight boat or a flight). How many times on this trip do you want to do this?

There are no right or wrong answers to these questions - just the ones that work best for you on this particular trip.

While Rick's Scandinavia book has great coverage of the places in each country he does include, he omits a LOT of each country, so be sure to supplement with other guides to learn more.

Harold - you bring up some good points. Ultimately I either want to do two cities, 3 days in each or one city and 3 day's of countryside or other cities.

In terms of Sweden, how would you spend 6 day's exploring and getting to know the country. I typically travel using a "platter" type trip, getting a taste of each city in a short period of time. I want a little less running around this time.

What time of year are you planning to travel? Do you want to do this by public transit?

A couple choices:
1) Stockholm and Copenhagen
2) Stockholm, Helsinki, Tallinn (using ferries)
3) Stockholm and the island of Gotland
4) Stockholm, Kalmar, Öland, and the glass region (works better with a car)

If it were me, I'd probably choose Stockholm, Helsinki, and Tallinn. You'd be able to take advantage of the overnight ferry which typically is less expensive than a hotel. You'd get a taste of three different cultures.

While in Sweden you should definitely check out the lake Siljan and it's surroundings. Nice scenery, beautiful buildings and very nice and genuine people. The red-house area is very-very Swedish :)

And if you care to get a bite of the best crispbread Sweden has to offer (and to meet one of the nicest guys in the whole country), then on your way towards Siljan stop for a few minutes in Stora Skedvi and look for Joel Lindblad's crispbread bakery (here you can find some more info abut him: https://story.visitsweden.com/meet-the-original-hipsters/).