Independent civilian visitors cannot access Kwajalein Island, so there is no restaurant scene to speak of for tourists. Eating on the atoll depends entirely on whether you have official access to the US military base.
For those on Kwajalein, the island has military dining facilities, a small supermarket, and a convenience store. The facilities are comfortable by Pacific island standards but are intended for base residents and authorised guests, not the general public.
On Ebeye, there are basic local food stalls and small shops selling packaged goods. Options are limited and the food is simple, reflecting the difficult economic conditions on the island.