Amata wrote:(2) a city with nearby small town/rural attractions that you could go to as day trips on the train. (Somewhere on LTH there is an old thread in which we all gave gleam advice about a trip to France, urging him to use Paris as a base in that way...). In other words, I wouldn't worry so much about whether the city itself has enough to see for a whole week -- I would think in terms of the whole region. (e.g. Nice as a base for the Cote d'Azur, smaller cities in Italy, etc.)
Stockholm is not as central of a flight hub as it should be; as long as you might be bouncing through Amsterdam, Frankfurt, or Paris anyway, I think picking a secondary, non-capital city or region makes perfect sense with the luxury of a whole second week. I agree with Amata that the Mediterranean would make a nice contrast, and Nice is a fantastic hub. You've got the coast, the mountains, a confluence of trading cultures bringing every food imaginable (including some excellent Moroccan), and easy train access to Marseilles, Aix, Provence, Monaco, and Liguria in Italy for eye-opening daytrips or overnights, and this is an area where you can live grandly or economically with equal success (and excellence of food). June falls between two festival seasons in the area and could be just right.
Nothing wrong with Barcelona or Prague, though. While I don't think you should be worried in any destination about language navigation (the world is tipping our way, lament it or not), there is something to be said for picking a central city and developing a relationship with a concierge or host that can get you around, out, and back with a personal touch and easy contact-ability. On that note, the best advice I can give is to call your credit card companies in advance to let them know you'll be traveling, and check in with your cellular provider as well to see what the options or restrictions are, to minimize surprises. Congrats and good luck.