Destination selection

You have only 6 full days. That could easily be spent all in Paris. If you absolutely must see another destination logistically easiest out of those you named would be Amsterdam because of superfast train connection. Then you should have open jaw: fly to Paris, fly back to US from Amsterdam.

No one can really answer your question except you. As said above, Amsterdam and Bruges are the easiest because they are a train ride instead of a flight. But if you don't mind a flight (and as long as you book open jaws, into Paris and back to the US from your other city), you can go anywhere you want. Of your list: I'd certainly go back to Paris, Bruges, Turkey (Istanbul, Selcuk, and Ankara; I didn't like Bursa), Portugal (Lisbon, Sintra, Santarem and Tomar; I didn't like Porto), Prague, and Hungary (Budapest, Pecs, Vac, and Szentendre; Eger was not so great for me). I haven't been to Greece. And I didn't care for Madrid. But that's my taste and opinions, not yours. In your shoes, I'd look at travel videos and read travel books (Rick Steves and others) to see what calls to you. Rick's videos are on Hulu and YouTube. If you want another destination within France, Lyon and Nancy are my two favorite cities there besides Paris, and with PREMS train tickets, getting there would be cheap too. If you are an Art Nouveau fan, Nancy is a must, and Lyon just has a very nice vibe.

Since you have so few days, how about staying in Paris the whole time, doing a few day trips if you're sure Paris can't entertain you for 6-7 days. Lots of options for day trips, although specifics would depend on your interests. Obviously Versailles is an option. Vaux le Vicomte is an amazing chateaux that can be easily visited on a day trip (and I much preferred it to Versailles since it's furnished and therefore gives a better understanding of life at the time; also, it's much less crowded and therefore easier to experience). Monet's gardens. Beaches of Normandy and other WWII sites interest some folks. Mont St Michel is lovely and can be visited on a day trip. Stunning Gothic cathedrals are accessible (Chartres, Reims, Amiens, Strasbourgh, etc). Strasbourgh and Colmar can give you a taste/feeling of Germany within France; if you want to visit them, an overnight would be best (and I'd stay in Colmar, just stopping in Strasbourgh for the cathedral). If you really want to visit multiple countries, I suggest picking only one other country, and flying home from that country (rather than from Paris).

Two ideas come to mind. Take the Chunnel Train to London for a few days. It's fast comfortable and not terribly expensive. We won't fly into Chucky D. Airport so we have flown into London on a couple of occasions and taken the train to Paris. Another idea is look for cheap flights anywhere out of Paris and "sample" some place interesting. We have done this with budget flights to places as diverse as Moscow and Jerusalem from cities in Europe. Both of those side trips were under $300 rt per ticket but with one of the European discount carriers like Wizzair or Ryan you can do it for half that.
In April we are flying RT to London to fly fish the chalk streams south of London. But I also got a real cheap RT ticket to Budapest and we will split our time between the two. If you do one of the sampling trips make reservations in Paris for the front end and back end of your trip and then ask the hotel to hold the bulk of your luggage while you go away for a few days.

I'd rather stay in Paris the whole time. Just too much to see and do. I would take a couple of daytrips, though. Versailles would be the most obvious being 20-30 minutes away, but there are multiple other options in all directions (Chartres, Reims, Giverny). I am actually planning to do this next December.

Since you have already been to Paris and indicated you do not want to stay there, have you been to any other locations in Europe? While all of the places you listed are great, it all depends on what you want to do. Are you flying back out of Paris? If so I would stay in France, take the TGV to Avignon, rent a car and see Provence and the Mediterranean. Otherwise, if you can still do an open jaws flight and want something exotic and very different from Paris I would go to Istanbul... It's beautiful and very reasonable and just about the exact opposite of Paris... so lots of diversity on your trip.