All of these are excellent destinations.
The problem with Europe is not to find great destinations, but to decide which ones you will never going to see in your lifetime. You could literally take an outline of the map of Illinois or Indiana, transpose it on an area on Western Europe, (say, England, or the Low Countries, or Northern Italy) and a lifetime wouldn't suffice to see every must-see within in.
To pick three or four European cities is impossible. I have no idea how non-Europeans go about trying to do Europe. I am nowhere near getting close to seeing the highlights and I've done Europe from the Polar circle to Gibraltar, from the northwest of Scotland to the southeast of Greece,
As coincidence would have it, I'm familiar with all your options:
Paris - my second favourite city in the world. Needs no elaboration.
Munich - My favourite city in Germany might be Hamburg. Actually, my favourite area in Germany would the Moselle Valley. Old German villages that look like blueprints of WS Germany. Same size too. Combined with old castles perched on mountaintops and the city of Trier, which mixes Roman monuments with Romanesque cathedrals and mediaeval German squares.
I think Europeans tend to go to Berlin. But it suffers from heavy damage, and is modern in many areas. Munich is where the Americans go. And rightly so, I guess. More unspoiled, more stereotypical German, situated in the most charismatic German region of Bavaria, the Alps in the distance. If you are only ever going to see one city in Germany Munich might be the best choice.
- London. Incredible. A sight to behold. London's claim to be the center of the world is as good as New York's. Maybe better. I was on Primrose Hill last year, with my London-based gf. It overlooks the center of London, and is also where the main characters of 101 Dalmatians took a walk. From there great walks can be had into Regent's Park, or up the canal to Camden Locks. Perfect day. ^_^
- Edinburgh. On my way to Edinburgh two years ago some American on the train was boasting how it was Europe's best city. Which I thought a silly thing to say. But I must say, Edinburgh's claim to be Europe's greatest tourist city is as good as anyone else's. Much as I love neighbouring Glasgow - fabulous and grand, Edinburgh is the more emblematic city. The more Scottish. From the center of town you look out onto the harbour, you can walk straight into the Highlands. There is a castle on the hill, there is an old town and new town (where you feel the famous Scottish Enlightenment). A perfect destination.
Be sure to watch Trainspotting I for preparation on local culture.
- Barcelona. Fantastic city. Although for my liking, however great Barcelona might be, even just on the Iberian peninsula I prefer Lisbon. This would be the one I'd skip if you have to choose. Yes, I realise half of Europe would have me burn at the stake for saying this about their favourite city.
- Amsterdam. The finest city in Northern Europe. By far the greatest of the smaller European cities. The center of the world in the 17th century world and it shows. Great to combine with London and Paris, and also with a few side trips to Belgium (Bruges is a mediaeval time-machine, my pick if you are only ever going to see one place in Belgium)
Prague, Vienna, Rome, Venice and Florence want to have a word with you...