Not an island, but a recursive geo-political region: http://en.wikipedia.org/wiki/Dahala_Khagrabari

There is such a thing in Rhode Island: https://maps.google.com/maps?q=41.916681,-71.411937&ll=41.91...

OK, the inner island and lake are man-made (hill in a disused landfill), the middle island is connected by a land bridge, so it's more of a peninsula, the middle lake is really a river and canal, and the outer island is actually North America.

One of my favorite recursive lakes is quite accessible to many on HN, it's at Golden Gate Park in San Francisco.

http://binged.it/1lLOpk1

See also: Lake Manitou, the largest lake on a lake island in the world.

http://en.wikipedia.org/wiki/Lake_Manitou

Here it is in Google Maps:

https://goo.gl/maps/be2Mm

Another in New Zealand, near Wanaka in the South Island: https://goo.gl/maps/ehUzh - there are some photos in the GMaps gallery too. It's a nice boat trip from Wanaka and a 15 minute walk up the hill.

Inception island.