Go for a walk in the park.
Pitch a tent, or a mosquito net in your living room and have an indoor picnic.
Visit a museum that is either always free, or has a free day.
Check in your local free entertainment paper to find out if there are any free concerts, classes, lectures, photo safari’s, bird watching tours, festivals, plays, wine tastings, hikes or other stuff like that.
Or, if your date is interested, you might enjoy (with the help of some internet searching) to do a walking tour of your city (Honolulu in your case, right?) in search of great architecture and public art, and/or history. My brother and I do this on a regular basis, mostly in Los Angeles and around southern California. Bring a camera.
Check this out Honolulu Public Art Finder
And Honolulu Magazine’s List of Best Architecture
And List of Historic Landmarks in Hawaii
Here’s a bunch of Upcoming Events (not sure which ones are free, you’ll have to click on them to get more info) on Oahu.
Here’s 101 free or less than $10 things to do on Oahu
Here’s some Free Stuff in Waikiki
Here is a list of Romantic Destinations on Oahu most of which are free.
Have fun Jake : )