I've always wanted to skydive

Why don't you try to do skydiving? Maybe you are scared; but, you should know that skydiving is a good way to feel excited and happy. You can forget your problems and your stressful life.

I've never done any kind of extreme sport; but I think skydiving is an opportunity to overcome my fears and to feel fine with myself.

When I am older I'd like to say that I've ever done a dangerous sport. Do you like my idea?

It is true that skydiving has a high price; but seeing your city from the sky, being wonderful, is worth it.

You may not agree with me; but I think all people should to do new and scary things in their lives.

You can say "I've always wanted to skydive" or "I've always wanted to go skydiving."

"I've never done any kind of extreme sport" could also be "I've never done any extreme sports".

"If I were older I'd like to say that I've ever done a dangerous sport" is the correct version, but "If I were older" is talking about if you were older right now.

"Would you like my idea?" isn't grammatically wrong, but it's asking if we would hypothetically like your idea (which in itself is hypothetical). "Do you like my idea" is enough.

"...is expensive" is much quicker to say than "...has a high price".

"Is true that skydiving has a high price, but you can imagine to see your city from sky, it may be wonderful" is really three seperate statements with no connection between them. Either separate them into difference sentences, or make them relevant to each other. You can say something like "Is true that skydiving has a high price, but the wonder of seeing your city from the sky is worth it" (where 'it' is the high price).