What are some benefits of getting your private pilots license?

You can fly yourself from place to place.

There’s more to it beyond the obvious ability to fly.

Think of it as becoming a member of an exclusive club. The license shows you have the financial resources, the necessary amount of time, and the required skills and intelligence levels.
If you have the chance, do it. Once you have a family and kids it will only get more difficult.
The people you meet while doing it will become your new friends.

Being able to fly even when you’re not on drugs.

Welcome to Fluther.

Aside from the license itself and the opportunities that it opens up, @worriedguy has given you the response that I would have: even if you never fly a plane on your own after you get the license, it still represents an educational / personal achievement. I don’t fly, but I have chartered sailboats. I would imagine that the feeling of confidence that “I can do that if I want to” would be similar to the feeling that I get when I pass a marina (where I don’t own a boat) and realize that I could sail any one that’s there.

My husband is a pilot and my usual answer is that I like getting there fast. I love watching the LA traffic backed up as I fly overhead.
It is a lifestyle, and something that requires you to keep your skills up. You can never get arrogant about it and take your skill for granted. Most accidents are pilot error (or a mechanical problem that could have been handled but BECOMES pilot error) and they usually happen when people get over confidant in their pilot skills and stop relying on their check lists and training.