Review: Google Nexus 4

It has automatic brightness but, you have to keep an eye however on the applications that run on the background as well, you have to adjust how often your email account syncs, your social network feeds update and which radios are on.
The battery life of the phone is not that bad if you tweak these a little bit. (it will last about a day), the display is one of the last things to worry about, it is all bad power management on the software side, the battery itself is big enough for the phone.