I think it's great you want to stretch your wings out and fly.
I also think you should draw up some real plans.
Start by getting your relatives contact information and getting in contact with them. If you had a great roomie while you were in school, you should get in touch with them as well. Start by just saying hello, asking how they are, mention what you last remember hearing about their life from them, ask what they're doing now. Ease into it all slowly. Most of the time, small talk is pretty useless and annoying, but in this case, it's your friend. Use it to figure out if they are still the same people, use it to figure out their living situation (to see if living together would be feasible/mutually beneficial), use it to figure out if regular contact with them (let alone living together) would drive you bonkers. Use Facebook to get in touch with them. As long as you know their name and face, it'll work and it's free.
Figure out where you want to live and what you could afford to rent. Don't forget about parking, public transportation, food, library distance, crazy neighbors, crime rate, or anything that is of unique concern or interest to you.
Get a job as close as possible to where you want to live. This one's easier said than done, and should be done before you move- at least in this economy. Maybe you could guide tours at the local science museum. Look at city jobs and federal jobs- right now they tend to pay better than private jobs, at least that's been my experience.
Break the news to your parents only when you have all these things in place. That way they'll know you've thought this out. They'll feel more comfortable if you have a plan, a job, and have already crunched some numbers and have pictures to show them. You're their baby. It doesn't matter if you're 5 months old or 25 years old.