I've been to Belgium. Other than the central core/grand plas area, Brussells is nothing special but Brugge is gorgeous. Lovely canals, excellent shopping for the ladies.
Barcelona is simply beautiful. huge long plazas, great shopping, amazing architecture. Lovely climate (on the med.) wonderful beaches. Very cosmopolitan. Superb food. Clean. Generally safe.
Paris is beautiful and HUGE. It is almost overwhelming in size. Lots of things to do/see there. French people would hate this characterization, but there is something almost american about it in some ways. It is a city that is well organized, excellent services/public transportation, Honest/well regulated cabbies. you know what you will be charged for your lunch, as opposed to going into negotiation mode like you do in.....
Rome! Ya, you're going to get ripped off by cabbies. In the ancient city, the food is, uh, bad, in the tourist areas. Shops are expensive. Not the cleanest place. It's full of Italians, so you know it is NOISEY. Traffic is absolutely insane, you will die if you step off a curb at the wrong time. Heck, you may get hit by a car while you are still ON the sidewalk. Hotels are almost as expensive as Paris. And yet...
Rome is, by far, my favorite European city. If you stay in the ancient City, you will be immersed in the foundation of western civilization. The ancient city core is quite small. Rome was not a big city until about 200 years ago. If you stay in the area of Campo de Fiore or Piazza Navona, you can walk in less than 30 minutes to the pantheon, the colosseum, the spanish steps, the Roman Forum, Piazza del Popolo, the Vatican (St Peters and it's amazing museum), Trevi Fountain, Castel San Angelo, the Tiber Bridges. just walking around the corner you may find yourself in front of a Bernini scupture, a Rafael painting just hanging church as decoration, a fabulous fountain, etc. It is a feast of sights sounds and smells. Perhaps the liveliest city in Europe. Take advantage of some of the excellent tour companies. Ask a local where to eat. Stay at a VRBO property. Take the Leonardo Express from FCO airport to downtown Rome (hang on to your wallet... pick pockets.) Take a train to Florence, or Napels / Pompei, or cinco terra. Really good shopping, but expensive. I promise, the kids will never forget their stay in rome.