Several visitors in the past have inquired about local luaus that are not primarily tourist shows. Local posters have suggested that church fundraisers are more likely to have better food and the opportunity to enjoy a local ambiance. The best known is the Kaumakapili Church luau in the summer, near downtown Honolulu, which I have enjoyed taking visiting guest to when the timing worked out. Often, these events will offer both a sit-down meal option or a take-out option.
The Pali Lion's Club is holding a luau April 28 to celebrate its 50th anniversary, so if anyone is in town looking for this type of event, here is your chance. I can't vouch for it personally, but the food is coming from Young's Fish Market, which often gets good reviews on this site for its Hawaiian chow.
St. Anthony's Church
148 Makawao St
Kailua (Windward O'ahu) 96734
Tickets are $35, includes pupu, meal, Hawaiian music, and door prizes. Not sure if there is a take-out option for this one. Be forewarned, the beverage provided may be nothing more than a kool-aid-like overly sweet drink, but you can probably ask for tap water. Never hurts to carry a bottle of water with you just in case.