Matsumoto's
North Shore - best strawberry flavor, get it with ice-cream and
be careful not to knock it over with your bionic tongue. 
If you look on the ground you will see the puddles of shave ice casualties.

Waiola
Waiola is in "town" in Honolulu and has a similar shave like
Matsumoto's but have their own flavors and unique atmospher. 
It has been considered the Nazi Shave Ice due to their strict ordering rules.
There are two locations go to the original on Waiola St.
and avoid the other location on Kapahulu.
 

Ice Garden
This is the smallest shave ice place, with just 8 chairs to sit. 
Two ladies run the shop and have been for over 30 years. 
The shave here is fine but not as fine as Waiola and Mastumoto however
what they lack in size they make up in variety.  The menu has over 30 choices. 
My favorite is 26 a mix of tapioca, chocolate, mochi-balls and evaporated milk. 
This is a must do for the serious shave ice connoisseur. 

Located in Aiea Shopping Center near Aloha Stadium
5 minutes from Arizona Memorial
990115 Aiea Heights Drive
Aiea, Hawaii 96701
808-488-5154
(map)

These are the three shave ice places I would recommend. 
Shopping center or drug-store shave ice should be avoided, it is just not worth it.