Depends on what area of NJ you are looking to move to:
In northern NJ, near NYC in Bergen County, ENA, Paramus.
If you are moving to Northwest NJ, Northstars. There is also Indigo, which I think is in New Providence, NJ. As far as I know, it is a relatively new gym, but seems to have a strong program.
Near the Jersey Shore are Devlin, Monmouth, Classic and Action. All good gyms and all have competive teams.
Also Rebound, and Head Over Heals in Northern Monmouth County.
In the Princeton area, is Arena (BEAUTIFUL gym) and has strong teams. There is also Willmoor, a little farther south.
Good luck choosing a gym!