I've been searching for places to satisfy my random bubble tea (and sometimes shaved ice) cravings for a while now since I've moved from LA, and I've found a real neat place in Bayside... just south of 73rd on Bell Blvd. The store is called Sweet Adele's, and is owned by a nice couple who told me they've been there for over 20 years. They have candy, chocolates, and Japanese snacks (including California rolls for 2.50, natch!) as well.
The bubble tea that I got is the cheapest that I remember paying, and the flavor is very authentic and most importantly, the bubble/boba/tapioca balls are the perfect chewiness (I'm sorry, I'm kind of a freak when it comes to these things- I hate a stiff, nasty tapioca ball in a diluted bubble tea drink). Also, they had a Shaved Ice machine that was the same as the ones I've seen in Hawaii... in flower cups like Matsumoto's! They have a lot of flavors also, and red beans/condensed milk on top if you like.
I also had a nice cup of coffee, fresh ground and brewed for less than the Dunkin Donuts a few stores down (why would anyone go there?!?!)... check it out if you're in the area!!