Making new friends and connections with other people. The more time you spend in one place, the greater the chance you can develop new friends (or possible romance?) with another person.
Taking a peek at the local lives. I have been invited to weddings, dinner and many other activities because of the connections I have made with locals
Learning the language. Especially if you decide to travel in an area that is not popular with tourists. Many times you will be required to know a few key words or sentences.