We have spent a total of many months in Waikiki over our 5 decades of travel. Here are some admittedly unusual touristy things that we do:
Shop at the Ross stores. For some unknown reason, we always seem to find clothing to buy there, unlike on the mainland.
Visit a Costco (our favorite is in Hawaii Kai) because the selection of merchandise is unique to the islands. Bring back bags of Kirkland honey roasted mac nuts.
For the best macadamia nuts, albeit at a high price, buy from North Shore Macadamia Roasters - only sold at their store (which they have unfortunately recently turned into a touristy place).
While you might go to Matsumoto Shave Ice due to its popularity, better shave ice can be found at these locations:
---Aoki's shave ice, just across the street from Matsumoto - note they have unusual business hours
---Island Vintage Shave Ice two locations in Waikiki - lines can be long at the kiosk location, but are shorter at the store location. Expensive.
---Shimazu Shave Ice - some homemade flavors -try the durian flavor syrup, if you are brave
North Shore Trading Company -across from Matsumoto shave ice for high quality Hawaiian-themed kitchen towels and other items
Poke bowl at Foodland supermarket in the Ala Moana shopping center - good value, although they have eliminated some of their toppings recently
KCC farmers market on Saturdays-huge and popular with locals
Any event that suits your fancy at the Blaisdell center - great sound system and semi-reasonable ticket prices


Finally, be sure to book a reservation to the Arizona/Pearl Harbor memorial. This is really the only tourist "must do" that we would recommend.

Aloha!