Most of the things listed below are free or inexpensive...
-take her to the Stadium Mall swap meet. They have a lot of neat stalls. I think they're open on Saturday mornings and Wednesday afternoons. Google it to be sure. If you're coming to Pearl Harbor then you could do the Stadium swap meet on the same day since both sites are so close to each other.
-Go to the Nuuanu Pali Lookout and see a panoramic view of the Windward coast. The Pali Lookout is just before the Pali tunnels on the Kailua-bound side.
-Walk through Chinatown. They have noodles factories, Chinese medicine shops, lots of good hole-in-the-wall restaurants. I love Pho To Chau on River Street for great Vietnamese beef noodle soup. It's so good. The owner is a bit like the Soup Nazi on the Seinfeld TV show.
But it's part of the charm of eating there. Chinatown is also a good place to get inexpensive souveniers to take back to the Mainland.
-Watch a traditional torch lighting and hula performance on the beach of Waikiki near the Duke Kahanamoku statue at sunset.
-Visit the lei shops on Maunakea Street in Chinatown.
-Go to the Honolulu Academy of Arts. Lots of good things to see there. The last Friday of every month the Academy has Art After Dark from 6pm - 9pm there's cocktails, food, and art. A lot of my friends go to it. It's a nice gathering of people, art, conversation, and food.
-Go to one of the local farmers markets. I like the Kailua Farmers Market on Thursday evenings from 5pm - 7pm at the Kailua Long's parking lot. You could also try the Farmers Market at Kapiolani Community College in town. That market opens Saturday mornings.
-Visit Iolani Palace and see the USA's only royal palace
-Make sure to eat a local plate lunch, shave ice, li hing mui (salty red pickled) snacks, and if she's adventurous have her try poke, sashimi, and poi.
I like the plate lunches at Kakaako Kitchen at the Ward Center shops in town. Ward Center is off Ala Moana Boulevard.
-If you drive around the island be sure to eat at one of the shrimp truck places. The plates are a bit pricey ($10-$11) but it's something so many visitors like to do. We like Giovanni's shrimp truck. I think it's the original shrimp truck. The rest came afterwards. You can't miss Giovanni's truck. It has graffiti and signatures galore from all the visitors.