[mkamionka]

Hi Paul,
I think it is possible to stay on the island. There is just this little town which you can spot in the photo. They have plenty of restaurants and I believe some little hotels as well.
I think it would be great idea. There are amazing hiking options and stunning beaches there. Of course it would be awkward to stay on La Graciosa without first seeing Lanzarote itself. It is a bit like going for a trip to New Zealand without seeing Australia before.

Kind regards,
Mariusz