If you take a right at Rigel, go up four dimensions and hang a left, you'll hit the Seventh Dimension Bar and Grill. This little joint is where all the characters hang out when not starring in a book, movie, show, or fanfiction. The 7th Dimension Bar and Grille has food and music for all races and species, with booths and tables for all and sundry.
Take a character from the HP verse and send them on down. Write about who they meet, who they talk to and what they say. Remember, they're not in any world, this isn't a crossover. The characters are just hagging loose for a while between adventures.
See you there, and do save me a slice of the 7th's B&G's famous huckleberry pie.