Norway is nice because it saps Germany of 8 IPCs (3 for the territory plus 5 for the NO), while also opening a sort of ‘back-door’ route into occupied Russia, but it’s harder to reinforce and build up a base in. If the Americans land on their turn then the British reinforce it that same turn, it could be all right. Certainly, having an American IC so close to Berlin will be very threatening for the Germans, and they will be forced to spend quite a bit of money on protecting themselves from bombing raids, bombing the American IC, or building transports, which is money they can’t afford to divert. However, Norway is just too remote to deliver a crushing blow to Germany.
Normandy is probably my personal preference, for a couple of reasons. One: free factory! Putting 3 tanks down every turn is definitely a big plus! It also serves as a major diversion for Germany, as Holland (which will leave West Germany exposed if in Allied hands), Paris, and Southern France (which will leave Italy exposed if in Allied hands), are all within American reach. The British are also in an ideal position to ferry units across the Channel. The one major issue I have with Normandy is making it last. It’s fairly obvious to the German and Italian players that you’re on the way, so they’ll have time to bulk up the West. But if you can put down a 3 tank build and get British reinforcements, you’re in a good position.
I don’t really like Southern France, because the Axis are just in such a good position to counterattack. The Italians can throw massive amounts of equipment at you, relieving the pressure on Germany. And speaking of Germany, a few tanks in Western Germany, Normandy, or Paris can bring an end to Southern France very quickly. Nevertheless, a landing in Southern France does have its advantages. It constitutes a first-rate emergency for Italy, costs them an NO, and again, ties down German IPCs.
So ultimately, Normandy is the best. As long as the British and Americans co-operate, the Allies will have a beachhead turning out plenty of tanks. Eventually, they can take Southern France and once they can afford to not use their IC anymore, Paris. Once Paris is liberated, Germany will be fighting a very uphill battle.