Run the wire through the back of the cabinets and install an outlet in the end cabinet below the counter top as long as the overhang is not excessive.
NEC 210.52 A receptacle outlet shall be installed at each counter space 12 inch or wider, and at each island counter or peninsular space 24 inch by 12 inch or greater. Receptacles shall be located not more than 20 inch above the countertop, or where mounted below a countertop less than 6 inches beyond the support base, not more than 12 inch below the countertop.
NEC 210.52 At kitchen countertops, receptacle outlets shall be installed so that no point along the wall line is more than 24 inch measured horizontally from a receptacle outlet in that space. Countertop spaces separated by range tops, sinks or refrigerators are separate spaces.
Won't I need a metal box on either end to properly terminate that?Use 12/2 AC cable along the back top edge.
This is where you have to start reading between the lines of the code book(the canadian one is the same way) It says any point on the counter has to be within 24" of a plug. Imagine a point with a plug 24" to the left and 24" to right you are meeting the code. This puts your plugs 48" apart and not 24".Am I required to have outlets every 2ft on the peninsula or is one at the post ok?
Yes, but you asked the best way. AC is flexible and offers more protection from a loose fork or knife in one of the drawers. But you can use Rmx since you have plastic boxes now.Won't I need a metal box on either end to properly terminate that?