Personally, I would hate to walk in and be forced to walk through that narrow gap between the island and the cabinets - the zig-zag orientation around the closets may even make moving decent sized furniture into the apartment near-impossible.

I would push the island to the wall and make it a peninsula, leaving 6' for you and your guests to enter the apartment - if you have to have custom cabinets made a bit shallow so that it will fit, you'd still be better off.

As far as everything else - I would consider pocket doors for the entrance to the bedroom and the bathroom...
...and rather than closets for the bedroom - I would specify a space for a builtin wardrobe system with drawers below and hanging above and shelves for shoes, sweaters, etc...
,,,and custom cabinets in the kitchen rather than the closet and pantry - Similar, with drawers below, some hanging above and adjustable shelves, etc for your pantry & other storage needs. It might also be nice to have a curved end to that cabinetry wall rather than a flat wall - it could have curved cabinet doors & drawers top and bottom where you could store your umbrellas, bills, checkbook, etc - and an open shelf or two where you could stash cellphones, keys, wallets, sunglasses, mail, etc.

These are very helpful comments -

I like the idea of having an island where I can entertain and have it be an extension of the living room as I would want people to enter from both sides. I considered the peninsula concept.

I was considering putting in a dining room table north of the island which prevented me from moving the closet. (Im not sure where else to put the closets.)

I will consider pocket doors.

Can you define custom cabinets rather than closet and pantry?

Great call on the curved portion!

Thanks

Is there any reason that the island has to be fixed in position if it doesn't have plumbing?

^^ That might be a great solution right there! Have your island on wheels so it can be moved to the wall when you're alone, but pushed out into the center when entertaining.

As far as the kitchen cabinets in lieu of closets: I would do a double-row of 12" high deep drawers along the bottom with doors above: hanging space in the center (closet) with shelves above behind the doors - deep shelves on the left all the way up, again behind doirs - and your curved entry storage/drop-zone space on the right.

BTW - The Feng-Shui for the space appears to be really, really bad for Relationships/Marriage and Knowledge/Spirituality Since those areas don't exist in your floorplan - and for Fame since the bathroom (water) is where the element for Fire should be

Definitely call in a Feng Shui consultant to help you choose finishes and materials that will help resolve those issues. My guess is you may need big mirrors on that blank kitchen wall and across the entire bathroom wall above your sink & toilet, and you may need to consider red tile for your bathroom...

Given the constraints of the unit, I'd say the primary problem that needs fixing is the closet/utility closet just opposite the entry door. My suggestion would be to narrow the opening to the living room, to allow sufficient depth for including these uses along the wall opposite the entry.