I usually like to put a small flourescent light over a sink Ken. Usually you can tie into a source of electricity in the attic. I like to drill down into the inside of a cabinet and install a surface mount outlet. The positioning of the light should be so that either the sink valance overhead or the light itself helps conceal the wire/plug and you can cut the cord next to the plug ( leave at lest 3" if possible) feed it inside, re-attach the plug and use the new outlet as the power source. ...»

There is a product called wire mold. its a plastic pipe that is flat and can be painted to match any decor. The big box stores carry it and its fairly cheep

I've run a handful using the power source for the range hood or overhead microwave, New LED lights are often low voltage which means a smaller wire size. I have run these inside the cabinets , along the front face frame...so they are invisible when looking in. A hot glue gun can "tack" the wires at periodic intervals so no mechanical fasteners are needed.

Another route is the battery version of LEDs...Leds use so little power that these battery ...»

Fluorescent lights will give a blueish, purple tone to your kitchen while the little "Hockey puck" lights will be a crisper and truer light. They are also available with a dimmer. They can be routed around your cabinets as well. If you have open space above your cabinets, it is nice to place them on top and let the light bounce up off of the ceiling.

Low voltage LED light strips are perfect for your application. An Internet search will get your the best price. Be sure to use warm white for that soft, natural look. I just used these to make a lightbox with shadowbox moulding for a picture-framing job. We'll e replacing our kitchen under-cabinet lighting with these LEDs.

I've used puck lights. Very nice, some have several light intensity settings. When I had my home built, I had outlets placed above the cabinets. In your case, try as mentioned above, use microwave/range hood, or wiremold to cover the wires.