Travel
We recommend you stay anywhere you please, but considering one side of the island is about an hour and a half away from the wedding site and most of the wedding party, we recommend you stay in the Poipu/Koloa area of the island.
For airline travel again, choose whatever you prefer, but Southwest has very affordable roundtrip options flying directly into LIH (Lihue Airport in Kauai).
Recommendations regarding where to book your stay while on the island
Airbnb
VRBO
Koloa Landing Resort at Poipu
Grand Hyatt Kauai
Marriott's Waiohai Beach Club
Sheraton Kauai Resort
Ko'a Kea Resort on Poipu Beach
We also recommend CostcoTravel for booking - they have options that include rental cars so you aren't trying to find the one Uber driver on the island, they also have locked-in rates for the resorts, and payment options available.
Majority of the wedding party will be staying at Koloa Landing Resort
Info below