Here are some great places that I would recommend getting a bubble tea in Central Jersey, in no particular order. This list will be an ongoing expanding list.
Gong Cha (Edison, NJ) - They make great milk tea, coming from experience of having worked there.
Sunmerry Bakery (Edison, NJ) - Mostly known for their bakery (get the cream puff), you can also get some good bubble tea at this joint.
Kit Tea (Highland Park, NJ) - A nice play on words on Kitty, this place has a great variety of drinks.
Kung Fu Tea (Edison, NJ) - I have frequented this place often and their selection is great.
Truly Yogurt (New Brunswick, NJ) - Mainly a yogurt joint, this place also makes a mean bubble tea. I prefer their smoothies with yogurt.
Mr. Wish (Edison, NJ) - A place with a nice relaxing atmosphere, they make a mean bubble tea.
Surreal Creamery (New Brunswick, NJ) - This place is known for their crazy concoctions with bubble tea and ice cream. You will be impressed by the creativity of their drinks.
Let me know what other places you think belong on this list that I should try or places around you that you would recommend.