North Shore has the best shore diving, but we're coming up on the end of the season. I would say that there's a couple of weeks left of predictably good conditions - after that it becomes iffy, and after September, forget it until spring.
The main shore dive sites on the North Shore are Shark's Cove, Three Tables, Firehouse and Waimea, which are all pretty much right next to each other along the coast.
Make sure you get there early to get parking - it's full by around 9 a.m. - then it's a pain to get your gear out of the car, the walk to the entry is longer, etc. Shark's Cove has a rock wall that's nice to set up your gear on w/out getting it all dirty and sandy. The other sites if you want to avoid that is out of the trunk of your car.
Waimea, Firehouse and Shark's Cove all have small parking areas and restrooms. Three Tables is parking on the side of the road. It's really crowded on weekends - if you can go during the week, that's your best bet.
Have fun!