For oriental supplies, including some japanese items (not sashimi grade) I make the trek up to Broadway supermarket. There are some other similar shops close by - this is near the Argyle "North Chinatown" , but I have found that this place has better selection, and (seemingly) turnover.
They do have several brands of unagi.
While you are there, do go up a few blocks to Argyle St. and buy a snack, and or noodles in the tiny shop right under El tracks. (Don't know the name).
The Bahn Mi (sandwiches) at Ba Le Bakery at Broadway & Argyle are very good too.
Broadway Supermarket
4879 North Broadway Street,
(773) 334-3838
Ba Le French Bakery & Restaurant
5018 N. Broadway
773-561-4424