Although June admission might be available at a small percentage of schools, the more common entry point is late August/early September for the Fall semester, or possibly early January for the Winter Semester.
I would recommend taking the GMAt as soon as possible, becasue it will take a little while before the official scores will be available and you will need GMAT to send them directly to the schools that you will be applying to. Also, with the holidays coming up, there may not be as many dates available and score delivery might be slightly delayed. Some schools have early deadlines, so you will want to find out when all of your documentation needs to be in. The schools normally do not make "exceptions" so you will need to make sure everything is in on time to be considered.
Here a few university search sites:
http://www.petersons.comhttp://www.studyusa.comhttp://www.gradschools.comGood luck!