I have a cordless keyboard/mouse combo and I love mine.
I think the
Logitech Cordless MX Duo is the best out there. The mouse has a base that recharges the batteries, and the keyboard does need two AA batteries. I put a pair of batteries in my keyboard back in January when I bought mine and haven't needed to change them. Just get some recharge-ables so you won't have to buy batteries ever again. It'll cost $82, which is kinda pricey, but I think it's worth it.