How much time do you have?
I hope at least 8 weeks.

Every part of Europe has outdoor activities, architecture, food and scenery. So you will need to eliminate destinations on some other basis if that is what you are looking to do.

I would think the best use of your time would be to try to learn as much as you can about today's Europe and the European Union, which would involve socializing with Europeans. Consider the kinds of apartment-share stays that are available through Airbnb where you have hosts, plus doing some research about interesting places to hook up with locals rather than just fellow tourists. The rest (sightseeing, good food and outdoor activities) will fall into place. Make some friends for the next time you return.

I would be most interested to talk with citizens of Madrid, Barcelona, Rome, Munich, Vienna, Amsterdam, Copenhagen, Oslo, Liverpool, Dublin and Reykjavik.

PS: I'd rather go to Athens than Reykjavik or Oslo for a European tour.

Please give advice What would be the best use of our time? Have we overlooked one?>>

as bob says, you'd need a substantial amount of time to see that lot - you could not be accused of overlooking any cities. but what you have overlooked is the countryside - Europe isn't only big conurbations but has much beautiful countryside as well, and in such a long trip, you run the risk of reaching cultural overload if all you see is the inside of museums and galleries.

also, you say that you are interested in outdoor activities - and for that you need to get out of doors! What about some walking, sailing, cycling? this would also be a good way of meeting some other people which IMO will not be very easy just touring from one city to another.

You really do need to get a guidebook or two or else do some serious research on the internet.

This is waaaay more cities than I'd try to visit, even in 8 weeks.

Not a city, but a small village in Austria. Good for a laugh if you happen to nearby: http://goo.gl/maps/WRLsB

Are you going by train and if going mainly to the big meccas many naturally want to do then IME trains are the best as cars are more and more liabilities in big cities - many Italian cities do not even let private vehicles into their city centers - many hotels do not offer parking - esp the cheaper ones and parking can cost $30 or so a day on top of $8-9/gal gas and predatorily high tolls on toll roads.

Trains are fantastic - going everywhere all the time - even to small towns and villages often.

Overnight trains link hundreds of far-removed cities so you can relocated long distances while you sleep and also save on the cost of a night in a hotel.

With those many cities - 10-12, which is fine IMO - then if going by train that much strongly look at some kind of Eurailpass - if under 26 then look at the bargain Youthpass - anyways for loads of great info on European trains and passes and planning a rail journey thru Europe I always spotlight these IMo fantastic sites - www.budgeteuropetravel.com (download this groups's free and superb European Planning & Rail Guide online for lots of rail-oriented itineraries in various countries); www.ricksteves.com and www.seat61.com.