I don’t think there is anything “wrong” with you. What you are describing isn’t that unusual for an introvert. Some people by nature need more alone time than others to feel comfortable and to regroup within themselves before re-engaging with others. Many people mistakenly believe that introverts are shy or don’t want to be with people. That isn’t true. They value deep relationships as much as anyone else. They just need private time to balance the drain of emotional energy that comes with social contact. I think you will find comfort in doing some reading about temperament (introverts and extroverts) on the web. That might help you be at peace with what you call your “grass is always greener mentality”.
As for your need for more meaningful conversation: Maybe you are telling yourself you need some more intellectually stimulating friends. Consider taking some advanced classes in art or philosophy (or anything that interests you deeply) or joining a book club (where people really talk about the books) or attending lectures that are offered publicly. Participation in such activities will help you meet people who will converse on the level you crave.
I wish you well.