I agree if you mean other direction is Asia, Australia, or New Zealand.

Non-american carriers are typically better, but I would take Business Class if it is a non-angled flat bed and save the miles from going to first for another trip in 2-3 years.

Europe does have charm, history, shopping, and culture. 10 days though is not a lot of time. Trying to visit several countries in 10 days is doable, but you will miss so much from the packing, unpacking, and traveling in between. I try to spend a minimum of 10 days in 1 country, but if this is a once every 10+ years thing then I can understand trying to see as much as you can.

I would take London over Paris. Barcelona over Madrid. Venice is a great city you can get the most of in only a day and night; it is romantic with lots of charm; and it is my wife's and I favorite European City for Romance and Charm.

I would use AA miles to get the air tickets. They are deal for Business or First. I too have been figuring out what to do with my AMEX points. I have about 300-400k. I've been thinking of using them to get the AMEX gift cards when they are 20% off. They seem to do this deal once or twice a year.