I suppose if your island is large enough (what are the dims?), you could drop a prep sink w/disposal in there.
Do you frequently have multiple people prepping/cooking in the kitchen at the same time?

The island is 8 ft x 3 ft. This home is only for two adults, and only one prepping at a time.

The place that "makes sense" for a prep sink is in the end of the island by the cooktop. However, that's really right next to the main cleanup sink, so it seems to me that it is redundant.

In my current kitchen, the cleanup sink is in the far corner away from the fridge and cooktop, with the island in between. I do have a prep sink in the current island that I use a lot, but I think it's because the other sink is on the other side of the room....

I'm trying to figure out if a prep sink is really needed given the layout of my new kitchen... I'm leaning toward *not* having one, but wondering if anyone here has reason to believe that my reasoning is erroneous and can show me the added benefit of adding one.

I would want one on the inside corner by the frig . Rather then have all my eating in a row on that side I'd do one at the far end and then 2-3 on the inside where planned

I have a small kitchen and I didn't do a prep sink at all in my kitchen. I don't need one. I do think that a prep sink where there is more than one cook would make sense but the three cooks at my house (me, myself, and I) are quite content with one sink.

How about the butler's pantry for a secondr sink? That's where my second sink is and I find it to be a very useful location. When I am hosting larger parties I often fill it with ice and then stash extra bottles there. If someone else is helping me prep for a dinner party it is great to set them up a little out of my flight path and between course it is a great place to put the dirty dishes if I want to keep my main sink open.

Can you swap the fridge and ovens? Then, I don't think you'd need a prep sink. However, if you decide to put one in the butler's pantry, it would work well with the fridge and pantry so close by.

If you did move the ovens to the area by the cooktop, that counter space would be a great place for granite or another heat-resistant material. Handy to be able to set cookie sheets right on the counter :)