Your post is timely for me. I have a 300BH that has the the outside kitchen and the little 12 volt lamp in the ceiling of the cook area doesn't cut it.
I don't have my trailer out of storage yet, but I recently purchased 32 feet of warm white LED strip, 4 strip connectors, power supply, and dimmer.
This might be hard to explain without pictures, but I'm running the led strip on the inside of the outside wall around the circumference of the kitchen door frame. Sort of an inversed vanity light.
I tested it last summer with some old rope lighting and it looked great, but the rope lights are decorative and not bright enough.
What's nice is it lights up the entire kitchen area including the drawers, cabinets, fridge, and sink, but no lights are exposed or hitting you in the eyes when using the sink our going into the cabinets/fridge.
I'll post pix after the install sometime in April.