ding, ding, ding... we have a winner!
Someone mentioned the Canon G series... smaller sensor, bigger body, slighly smaller price tag. The RX100 at the end of the day is the way to go.
But remember, you'll have to factor in a few additional costs. 1.) I'd recommend some type of camera sleeve, being able to throw it in your purse is one thing but naked it's subject to coins, pens, anything else metalic that could scratch or crack your LCD screen. 2.) memory cards are additional, instead of buying 1 large card spread out your data across a few in case a.) you lose it, b.) they fail (which they do from time to time).
Also, make note you'll need some form of advanced post production software. We all have the crap that comes with the camera or was free with our pc purchase but look into getting a version of Lightroom. I don't think you'll need something as powerful as the Adobe PS suite but Lightroom should be perfect and it's pretty cheap these days.
it's too bad the budget couldn't be extended slightly more, this is a great little micro 4/3rd's
http://www.bhphotovideo.com/c/product/842930-REG/Olympus_V204040SU000_OM_D_E_M5_Micro_Four.html