Adding pics in second post, of course.

This is the layout showing the freestanding island. In my imagination it seems to me prepping at the island is preferable to working in the space next to the sink as facing a wall seems claustrophobic.

I would get this base for storage.

And this base for the pullout. I just realized the pic is of a 24” deep base but I would get a 15” base. Ignore the door styles it is just their example.

It doesn't necessarily HAVE to be near the sink. In my primary home, my kitchen is small and I have a Simple Human trash can a few feet away from the sink.

In my Florida house, again a small kitchen but set up differently, I was able to have a pull-out trash bin. It is nice to not see the trash can in the kitchen but IMHO not a game-changer.

Not all the trash you throw away comes from the sink! You are emptying plates from the table etc. Your renters will get used to throwing it wherever it needs to go.

Since you have an open concept, my first choice would be the pull-out.

Totally!

My trash compactor is in my island in my L shaped kitchen, it is behind me when I’m standing at my main sink, so all I have to do is twist around to throw stuff in the trash from the sink, but I use it more when doing prep work at my island, so it works out great that way!

I just walked over to the space in question and walked off the pretend pullout trash. I think it will be very functional so will play with my floorplan program and change it to a built in island.

We bought an old house three weeks ago and are already trying to figure out how to put in a trash pullout. Haven't even moved in yet. We consider it that essential.

It is a rental. Even short term, I would not put a wastebasket in a cabinet. Renters tend to be rough on stuff.