The dishwasher is currently located in the most typical and logical location; however, as the "un-loader" of my family, it is nice to be able to access all of the cabinets with the dishwasher door open, so you could consider putting it on the end of your peninsula, but be aware that you would have to run a pipe for fresh water, a drain pipe, and power.

It should be close to the sink minimize the distance between wet dirty dishes and the dishwasher. Whether it's to the left or right is a personal preference. From my perspective, having the dishwasher door and the oven door but up to each other is NOT a good idea. Personally, I'd either relocate the stove or move the dishwasher to the other side of the sink, whichever is less expensive.