Being from that same region in New York myself, the weather/location of UCLA is definitely the major draw over Cornell. I'm just trying not to throw away a T-14 option for a few years of sunshine. Unless the two are comparable.... in which case I'll see you in Cali.
I think, honestly, that although Cornell is a T14, that it is still going to be mostly portable in the NE of the US. Which is great if you want to work in any of the big cities there like NY, Philly, Boston, etc.
However, I would be willing to bet that UCLA is the bigger dog in Southern California and in California overall.
I don't think the difference in reputation between the two is significant at all. Really. I wouldn't chose Cornell JUST because it was a couple of places higher in the US News rankings. Other factors like your extracurriculars during Law School and your class rank will have far more weight than a 3 place difference in the rankings.
If you'd ultimately like to live in SoCal, I'd say UCLA is the place to go. If you want to work in Boston or NYC, then Cornell. Even though the very top ranked schools are not really regional, these schools are sort of in the area where geography has an impact.