Post a phot. Good idea above, but sounds as though the addition of under cabinet lighting is also necessary.

You could do something like this it is an 8' peninsula with 3 drop lights

For some reason we did not want even visually divide kitchen and dining room with pendants. We ended up with

IKEA NYMÅNE ceiling lights.

I would go with some recessed LED cans for the lighting over the peninsula. They look clean and there would be no obstruction on your sight lines.

Its funny but those pendants I show are actually a nice look and in no way hamper the sight lines.

Patricia, those pendants are gorgeous and would totally work in the space. Where are they from do you know?

Perhaps, in lieu of pendants, something like this:

https://www.homedepot.com/p/Kenroy-Home-Corbis-4-Light-Bronze-Island-Light-93595ORB/300513035?cm_mmc=Shopping%7CG%7CBase%7CD27L%7CMulti%7CNA%7CPLA%7CInteriorLighting%7c71700000038836110%7c58700004241533705%7c92700035280099904&gclid=EAIaIQobChMIy96Bk8Dw3gIVjf_jBx0DyAHHEAQYBCABEgLtmfD_BwE&gclsrc=aw.ds

Another option would be smallish semi-flush lights, which would have some visual presence while staying close to the ceiling and out of your view.

Andante Industrial Semi Flushmount Ceiling Lamp, Brushed Nickel · More Info

1-Light Semi-Flush Mount, Brushed Nickel · More Info

Baxter 1-Light Semi-Flush, Burnished Bronze · More Info

George Kovacs Lighting P854-084 One Light Flush Mount · More Info

I prefer pot lights.

I know I love them too but no longer available and we knew that when I got them for that client.

Hi, we have several modern and traditional pendant lights that would look wonderful in your home! All of our fixtures are handmade in the US with high quality copper. Check out our website lanternandscroll.com we would be happy to help you!

I'd go for the cans but space them so you could change to pendants in the existing locations if desired in the future.