Masters in CS at Stanford

Hi,
I want to attend Stanford or Berkeley to earn a master’s in CS. I hope that someone here can give me a feel for my chances of admission, provide advice on what I can do now to improve my chances, and perhaps suggest alternative options. Background:

My current position:
-I graduated from a top 20 school not know for CS
-3.83/4 GPA
-BSBA degree, but finished a degree in math and almost a third in CS
-Had several 7 class semesters with tough courses (probability, mathematical statistics, stochastic processes, 2 courses on machine learning, bayesian statistics, cloud computing, 2 algorithms courses, linear algebra, real analysis, mergers and acquisitions, options and derivative securities, 4 general programming courses on java, c++, and scripting languages, etc.).
-No research experience
-No professor knows me very well
-This fall I started work for a firm that does a lot of heavy stats (math and econ focus), but not serious programming

Other relevant background:
-I entered college as an athlete, and that was by far my main focus. I did not know what I wanted to do until I serendipitously ended up working at an inspiring startup my sophomore year and saw Andrew NG’s machine learning videos. My classes were easy during my first 3 semesters, but I only averaged a 3.6 (didn’t feel motivated). My final 5 semesters are nearly perfect with much harder courses. I didn’t do research or connect with professors because I thought that learning more material and raising my GPA would get me farther, and that’s what I sincerely enjoyed doing. I have not done significant open source work, but I have been competing on kaggle and am rapidly improving - I enjoy doing it and am building a body of work I can present with my application.

Why CS masters at Stanford/Berkeley?
-I want to transition to working in the tech industry, preferably in machine learning, and a Master’s in CS could provide credibility
-It’s worth the monetary cost: I am saving up money to pay for part of it and hope to get a TA position to pay the rest
-I want to spend some more time learning all the time
-My significant other wants to move to CA where their family is, and I want to end up with them
-My best friends are moving out there
-It’s warm : )

I feel very strongly about this and a bit like I missed the boat and am am now chasing after it. Any advice to catchup to it is much appreciated.

Edit: GRE(M 800, R, 790)