Okiale as zahava said, look into NCSY. Also look into Bni Akiva, they have shabbatons. Make connections with people in those youth groups and stay with friends. Depending on the area you are in, there might be other organizations. Talk to your local Rabbi to find out if there other organizations that have shabbatons. I know Yachad has shabbatons for high schoolers (Yachad is an organization under the OU that promotes people interacting with special needs individuals. Yachad also has shabboatons for middle schoolers and communities.)
I went away to a dorming MO Yeshiva for high school, I stayed at my classmates houses every 3rd week, sometimes more. Staying with friends is a great way to get out of your parents house for the weekend.
147 – Theoretical question, if someone were to go spend a shabbos at your place, would the discussion be about different phrases and calendar dates? Are you secretly a baseball fan and talk about it all the time? What is a shabbos at your place like? Also can I be invited?