O'ahu on a budget

Several hotels have free hula shows in Waikiki including the Halekulani Hotel and the Sheraton Princess Kaiulani. Just order a beverage or dinner and enjoy. The Honolulu zoo and the Waikiki aquarium are 

At Kapiolani Park Beach and are inexpensive. Take the city bus to Pearl Harbor and take the free Navy launch to board the Arizona Memorial Museum Association .Best people watching is in Waikiki.

Aloha, Mireille! If you are looking for recommendations for Waikiki and North Shore on a budget, here are a few tips:

1. Try airbnb.com for accommodations. Typically much lower priced than hotels + you get a local host that can make recommendations too :)
2. Skip the overpriced mediocre chain restaurants and try local and more affordable favorites like South Shore GrillSouth Shore Grill on Monsarrat, Rainbow Drive-In just off Kapahulu past the zoo, Ono Hawaiian Foodsalso on Kapahulu, the KCC Farmers Market for fresh fruits, veggies, and ono plate lunch options on Saturdays mornings and Tuesday nights. Hula Grill Waikiki (right above Duke's) has a Happy Hour menu (one of the rare Happy Hour menus on the beach (not to mention they have a great breakfast/brunch and are one of my favorite places to dine for dinner. They are pricier than the other recommendations but you need one splurge night! Many of the restaurants near and on the beach get by on their spectacular view but serve mediocre dishes. Hula Grill has the view (ask for a seat "on the rail" AND some of the best food in Waikiki PLUS they use locally sourced ingredients as much as possible.
3. Luckily, the beach is free. So you can always go for a dip in the ocean! Check out Kaimana Beachand some of the quieter beaches near Diamond Head if you want to relax...or if you're looking to mingle, park yourself in front of the The Royal Hawaiian hotel or somewhere along that busy strip of beach.
4. Hiking is also free (or nearly free). You can get to the Diamond Head State Monument trail by bus or uber/lyft, or even walk there depending on your fitness level and where you are staying. It's just a few dollars to enter, a nice hike up (though it can be hot, so plan to go early and bring lots of water, a hat, and sunscreen), and it gives you a fantastic view of Waikiki and the broader Honolulu area. Manoa Falls is also beautiful and not too far from Waikiki. 
5. There are often free hula shows around Waikiki. Here is a nice one to check out that is right in the middle of Waikiki: https://www.tripadvisor.com/Attraction_Review-g60982-d2671501-Reviews-Kuhio_Beach_Torch_Lighting_Hula_Ceremony-Honolulu_Oahu_Hawaii.html
6. On the North Shore, you can find lots of great and affordable eats at all the little food trucks.
7. Just like in Waikiki, the beach is free! So go enjoy Waimea Bay Beach Park
8. If you are looking to meet people, my friends do a Boat Brunch in Haleiwa Harbor on Sundays from 11 AM - 1 PM

ENJOY!