I removed a prep sink from our island to have the solid surface for chopping, setting things down, serving, etc. I would plan the extra sink for the bar area to keep it out of the kitchen space. Your large sink is across from the island so you don't need two right next to each other imo.

If you prep on the island that is where you should put a prep sink.

I like my main sink to be strictly for cleanup.

Your island is large enough for you to have a prep sink and still have plenty of room for setting things down and serving.

I think it depends on how many people usually are in the kitchen cooking and how much you think the prep sink will be used. I'm a lone cook and don't really like people to help me in my space so every house I've had where the prep sink came with the house, it never got used. I much rather have the entire island for other uses like calidesign says. And as far as the bar sink.. how will you use it? I never use mine and I have yet gone to a party where people are using theirs. I'd put a drawer dishwasher instead in that space. As you clean up you can just pop the glassware in there without having to carry them into the kitchen and put them away right at the bar again. Save a lot of steps and it's always nice to have that extra dishwasher when entertaining. I just think you need to think how you live as the next person that makes a comment here could tell you how they love their prep and bar sinks. Enjoy your new home :)

Ditto what Mama Goose & Vinmarks said -- in the island, not the "bar" area.

KEY components to a functional Prep Zone are:

(1) direct water access and

(2) sufficient counterspace next to the water source (at least 36" of uninterrupted space) and, preferably, without the DW in the middle of it.

Putting a sink in the bar area will make it useless for prepping.

Also, put in a prep sink, not a bar sink. Bar sinks are much too small for prepping. They're designed for filling a glass of water or dumping a glass of water, not working in them.

Given the size of your island, I would put in a prep sink that fits in a 24" wide sink base.

We have one and I'm usually the sole cook now...and the prep sink is still very useful. In fact, it's used at least as much as the cleanup sink, if not more. It's nice not having to worry about whether there are dirty dishes in my way when I'm prepping. (FYI...it was even more useful when our kids were still home and helping prep or clean up. I got the prep sink and they got the cleanup sink (and they dealt with the dirty dishes! :-D ))

I agree 100% with Buehl. We have our second sink in the bar area now. When we renovate, I am putting the second sink in the island, and it will be larger than a bar sink—will fit a 24” cabinet. Right now, the bar sink is used for people to fill up drinking glasses and little else. Even though my cleanup sink will be across from the island, I think the prep sink will be a real help and much more useful than the bar sink near the living room.

If you want symmetry on the island, the prep sink could go toward the left (as you face the island), with the MW on the corner near the fridge, where it will be most useful. I hope that's a drawer model, and not a counter top model in a cubby. Trash beside the MW will be accessible to all zones, then wide drawers over which most of the prep tasks will be done. However, if you planned to store dishes in the island, this layout won't work.