"The only other place that makes sense is under the overhang on the south side (where my question mark is) Is that right? Will it be difficult to use the outlet?"

It is very likely an outlet as you have marked will not satisfy the code requirements.

The overhang is likely larger than allowed.

Limited overhang and not face up in a counter surface are two of the NEC rules.

Put a flush mounted receptacle on the long side of the island.

Is there a reason not to put one on the side you are working from? I'd put one on the end & one near the prep sink. In either case you want them on GFI circuits. If you can't have them on the east side then I'd put one north & south.

I am overseas. There are no regulations here about even needing an outlet on the island (so my contractor says)or where to place it.

My overhang is 15". The picture is not to scale.

Aside from the cabinet with the prep sink the rest of the work side is drawers so I don't see where it would go on the that side.

Any other ideas?

I'd put one on the front side and also one on the back side. Back side to me is the more crucial one, since we love to use our laptops on the island and it's nice to have power for them when the battery runs low.

But it depends on how you'll use the island ... if you aren't sure, do both if you can since the additional $$ to run the second outlet are minimal if you do them both at the same time.

Didn't think about putting one on the back for laptops. Nice idea.

Where on the front side would it go? There are only drawers and the one door for the prep sink. I need one near the work side when I use small appliances (stick blender, hand mixer, etc.)

Can you put it at the front of the side? I mean, the same place as where you have the question-mark, but just moved right up to the edge as far as is feasible? Then you should be able to access it easily enough from the front side. (Are you left handed by any chance? :))

taggie - I agree that probably makes the most sense. And yes - I am a leftie!

why not do something like this pop up?
http://www.mockett.com/furniture-hardware/catalogsearch/result/?q=PCS34

The prep sink is a good location - especially if you are likely to use anything powered like a food processor when prepping.

Where you can put outlets on the other cabinets depends on what is in them, whether they are framed or frameless.

Your island might be large enough that outlets are required in two positions. I thought that one was required every 4'. We were initially told that an outlet under the seating overhang wouldn't satisfy the code requirement, but we asked them to check with the county whether one right at the edge of the overhang would because our understanding was that it had to be within 12" of the top of the counter and one there would be. At least our county accepted it.

We put one on the false drawer front in front of the prep sink. That one gets used the most.

Here is the one at the edge of the overhang (similar to if you slid the ? in your picture as far to the right as possible):

If you have a drawer at the top of that cabinet, the side of the drawer might have to be lowered to clear the outlet. We have a cabinet with pull-outs there. We used shallow outlet boxes and there is a panel on the side of the cabinet so part of the depth of the outlet box sits in the panel:

Thank you for those pictures!!! They are so helpful and I am going to show them to my contractor!

cloud swift - does the outlet in front of your sink get splashed? is that an issue at all?

Fooglie, it doesn't get splashed. The counter overhangs it by about 3/4" so that shields it a bit.

You might want to check www.sillites.com for an example of a self-contained receptacle that can be placed unobtrusively on the working side of an island.