In South America there are plenty of high peaks that can be climbed without any red tape. Aconcagua requires a permit, but the second highest,
Ojos del Salado (6893m), can be climbed without one from the Argentinian side according to its page right here on SP. making it the highest outside of Asia that can be climbed without a permit.
Elsewhere in the Andes many high peaks can still be climbed with little or no red tape as well. Since it became mandatory to go with a guide when climbing anything serious I reckon that Ecuador is the most restrictive country, but most countries have no restrictions anywhere except that for peaks in National Parks you may have to pay for access to the park itself. And, yes, in a few cases you need a permit to climb the mountain of your choice.
I don't know much about the situation in Asia, so I'll leave it to others to comment on that.
In the Alps you don't need a permit to climb anything, including indeed Mont Blanc. But the Alps are much lower than the Andes. Elsewhere in Europe, only the Caucasus is higher. I know that there is some red tape there, but I don't know the details.
The second question, asking for recommendations of some good climbs, I couldn't possibly answer without knowing more about your background. But since you state that you're new to climbing, your best course of action is to go with more experienced people. A good start would be to join a mountaineering club near where you live, and go on trips with them. And before aiming for anything really high, you better get some experience under your belt.