It should always be next to the sink, never be between the sink and range. And the MW needs to be next to the fridge. And you need a range, not a cooktop and wall ovens. Your kitchen is too small for that.

Whoops, I accidentally hit the wrong button and I can't take back my vote. I've always had my dishwasher right next to the sink. Works great to prerinse and then move rinsed dish to dishwasher without dripping on the floor.

Next to the sink.

This are the other pictures of the kitchen. The one of the peninsula dishwasher is to give an idea of what moving the dishwasher would look like

In your case, I think I like it in the peninsula. Then you can stand in the corner with the dw open and unload into the wall cabinet on the right. With the dw right next to the sink, you are forced to unload into the cabinets between the sink and range, crossing into the cooking zone.

Either to the right or left of the sink would be the preferred location. However, I wouldn't place it right in that corner--you need a bit of space between the DW and the turn into the peninsula. And no microwave in that position--the usage of it interferes with opening the DW. It all looks too cramped.

What kind of floor are you installing? If vinyl or tile, I would vote peninsula, for the reason emilyam819. But if wood, I would want the DW right next to the sink. Less drips across the floor to worry about.

Vinyl flooring will be installed.

Next to the sink. With it in the peninsula, you'd have to turn around every time you wanted to put a dish into the dishwasher after scraping it into the sink.

Have you looked at the installation instructions for a dishwasher? How would you run the water and drain pipes to/from the dishwasher located in the peninsula?

Are there going to be stools at that peninsula? If that's a dining area, would there also be enough room for the table and chairs?

Given the small kitchen, that ginormous refrigerator is a hoot!

My daughter has a DW next to a corner, I despise the function of it. Both options are not ideal. I'm wondering if you could eliminate the countertop seating and/or extend the sink wall to gain more length to the right of the sink, so the DW is not so tight to the corner? Doing so would improve access to the wall cabinet above. I would move the MW closer to the end of the penninsula instead of the corner.

In either case you are setting the clean dishes on the counter first, then moving them to storage. The DW should always be next to sink, the cleanup zone takes precedence over putting away dry dishes and should function first.

If you were to remove the corner Pantry you might find a little more space for the stove wall and some visual relief from the proportion of the large ref and the "hefty" mass of that wall.