travel with older kids (20-somethings)

Have you considered camping? It is cheaper than a hotel and plenty of outdoor activity!

There is a camping section in the 2010 Europe Through the Back Door.

Early August is a great time to go north. Scotland, Ireland, Scandinavia, Northern Germany, Russia are at their best that time of the year.

Further south will likely be too hot and too crowded.

If outdoor activity is the focus, consider Switzerland, specifically the alpine regions. You'll have wonderful hiking, plus mountain biking, ziplines, canyoninging, paragliding, via ferratas, etc.

Everyone thinks Switzerland is so expensive, but it doesn't have to be. Stay in apartments rather than hotels, have picnics and meals cooked "in" rather than dining out all the time. We've had nice apartments for 4 to 6 people, ranging from 160 to 200 CHF per night. If we had stayed in one place for a week we could have found apartments for even less.

I took my 20-something kids there as a college graduation present, and they loved it. We've been back as a family twice since.

Another possibility would be the Dolomites---a gorgeous place with lots of outdoor activities. This area is quite different from the rest of Italy, so you probably wouldn't be repeating what you've seen before. You can save money by staying in apartments here too.

Go up North, the weather is perfect and not too crowded. Down south is packed and very very hot! I heard Norway and the fjords are beautiful.

Norway is indeed very beautiful. It is also just about the most expensive place I've ever been (vying with Japan in that respect). It would be very costly for a family of four.