zin pretty much summed it up; i also recommend planning far less exertion that you'd think acceptable, things in europe (with the heat, and queues, and traffic, and bullshit that doesnt work properly ..) always tend to become harder than you imagine.
just find one, or two places at most, to visit and try to settle in - find a nice place, hang out at local bars, try the local food (food really is the n1 reason to go to europe) .. and if you get the itch to go see something, go. do *not* plan over-exhausting tours which cram in as much shit as possible, they are counterproductive.
barcelona, i've been a couple times, it's nice but nothing special. i did like sagrada familia which, i hear, has been finally completed.
and hanging out in teh ramblas is fun, if you watch out for the shady characters. (they got some rather superb hash there, if you are into that kind of stuff)
but, it's not the most "friendly" place. i would much rather point you in the direction of paris.
now, paris, you could live there a year and not see everything. imho, i would dedicate the first 6-7 days of the trip to just settling in, tasting the amazing food, visiting places like the sacre coeur and montmartre, tasting some more amazing food, and possibly try to meet some expats - the formula for success.
yeah, you'd think wtfbbq, i dont want to go to paris and hang out with 'muricans, but expats know exactly what bits to show you so that you can see the real paris - or at least, that's the way to best enjoy rome, which is not that different of a city.
then do a few bus excurtions to the countryside. that shoudl give you a well rounded experience of paris.
mind the voleurs (pickpockets), they are not as common as they would make you believe, but if you look 'murican you run a much greater risk than someone who looks local. dont carry your passports with you. also, you ought to be able to use the local ATMs.
my idea is, that when you visit, you need to decide whether you want to be a tourist, or a friend. tourists see the sights, friends experience the city. imho, the latter trumps the former.