I am wondering why did we not invade through a neutral country such as Spain.

That would've been a very irresponsible move. Spain just went through one of the bloodiest periods (no pun intended) of its history and was still very unstable, with a dictator of its own running the country. If the Allies landed in Spain, Franco (the Spanish dictator) simply would've entered the war on the side of the Axis, and the Allies would thus have a whole new front to worry about. Remember that Franco was already aided by the Germans in the Spanish Civil War.

Also, if the Allies landed in Spain, they would have to cross the Pyrenees to get into France. Mobilizing such a large number of men, machinery and munitions would be time-consuming, thus unnecessary.

The Nazi's did not occupy France so wouldn't it mean a much less opposed invasion into Europe?

I think you meant to say Spain here. Anyways, once again, it would've been a rash move to invade Spain. It was a miracle in itself that Spain didn't enter on the side of the Axis. An invasion by the Allies would've pushed it over the top.

There were other options considered, but not Spain. Churchill lobbied for attacking through Yugoslavia. The idea was to fight along side the Russians and so help keep some of Eastern Europe out of Soviet hands. The problems were that Yugoslavia is very slow going and the Russians would just take more of Germany.

Another option was to bypass northern Italy and land in southern France. The beaches would be basically unguarded. But the logistics problems of supplying a large invasion force that far away would be horrendous. The reward potential was great since there would be almost no one between the invasion force and Germany. But supply trumps pretty pictures on a map.

Normandy offered the right mix. There were beaches that they could get tanks on, there were ports (though it took too long to liberate them), and it was relatively close to England so short supply lines.

If you want to fight your way to Germany the worst place to start is 1940s Spain. It's far, big, very mountainous, has poor roads, uses a different railroad gauge and its railroads are still damaged from a 3 year-long civil war. Imagine all the difficulties faced during the invasion of Italy, but worse. The best you'll get from that is tying a few more Nazi troops there so the Russians can take more of Germany and earlier. Not to mention the bad PR brought from invading a neutral nation and fighting a regime whose establishment many American and British voters had supported just a few years ago.

On the other hand, you have northern France that is really smooth, was taken in one sweeping campaign and lies right next to the German border on one side and the biggest unsinkable aircraft carrier available on the other - Great Britain.