Our stay in Motel Lili was absolutely perfect. The small town of Lihue is the best place for a longer stay, because you got about 1h north and 1h south to drive and see all the sights. After an already long trip with staying in hotels or Airbnb without BBQ or stove, we were so happy to be able to prepare our own food for a couple of days. There is a BBQ and an outside stove you can use and which work perfectly.
Issues that others pointed out are noices from roosters and the existence of ants. Firstly, before you arrive you get the info about the roosters and the recommendation to bring ear plugs, so if you're a light sleeper, bring them! The wild chickens are a tradition in Hawaii and you will meet them on other islands, too. Secondly, to avoid ants don't leave any food out. Put even coockies and stuff like that in the provided fridge and you'll be totally fine.
A big thank you to Susanne who manages Motel Lili and attended all our needs. If we're ever in Kauai again, we're coming back.