Sounds lik you need one of the Sony OLEDs. 11" and a HDMI input, sounds perfect, no problem at all.
Budget? What do you mean budget?
More seriously - Viewsonic has one under 16"...
http://www.bhphotovideo.com/c/product/560159-REG/Viewsonic_N1630W_N1630w_15_6_720p_LCD.html
Price is good, size is about as small as I've seen. Coby also has some, but it doesn't appear to support HDMI.
If it's just AppleTV you want to monitor, you may want to try a HDMI splitter before your A/V receiver to send HDMI to the monitor full time and to the receiver full time.