I have designed a few Yu-Gi-Oh! cards, and I want Konami to review them.
Is there a way to submit my designs so that Konami will see and consider them?
Konami has general contact information for their offices. However, I highly doubt that they will accept unsolicited card suggestions. There are a couple of reasons for that:
Konami has to date released 16 fan-made cards. Out of those, 15 of them were winners of contests that Konami specifically held, usually "draw a monster" contests open only to children. The last one, Tyler the Great Warrior, was a Make a Wish Foundation wish for a 14-year-old cancer patient (who ultimately survived). As best I can tell, all of these fan-submissions were only for monster designs and not for card stats.
Given this, I think your chances are practically zero for being able to show a card to Konami. Your best bet is to participate in one of these fan contests they have, or if you are an adult, convince a child to draw a monster that matches your design.