Your career goals are going to dictate what schools are best. If your goal is to transition into a new type of investment vehicle, you will need to attend a strong finance school with a pipeline directly into those types of shops. Tuck stands out for having long-standing relationships with a lot of PE firms. Wharton is of course a top choice, but your GMAT score will hurt and your lack of ECs will hurt even more - Wharton is extremely focused on community and innovation within that robust community. You might want to consider Yale closely - very good finance program, plugged into Wall Street. Booth sort of goes without saying. But you are also going to want to consider some schools outside of the top 10, such as Tepper.
Now, if you go the other direction to make a career change into strategy consulting, you need to find a program that has a solid recruiting presence in that space, but that is also tolerant of career changers. This rules out Columbia real quick (in fact, even wanting to shift from what you are doing into PE might be too rich for Columbia's blood). It also rules out some of the other more traditional finance programs. Really, to me, there are two schools that stand out: NYU and Haas. NYU has programs designed specifically for people making career shifts like investment banking --> consulting. I believe it is called IMI and it helps you get plugged in from day one. Either way, it is a school with great ties into all investment sectors, but also is open to people making radical shifts. Haas has an overall approach to the process that suggests an open stance regarding people shifting careers.
Overall, your first step will be figuring out which of these diverse career angles is your priority at this moment, so that you can be singular in your focus on the applications. From there, it is about building a nice mix of schools that accommodate either pursuit (in case you change your mind) and that give you the best chance of gaining admission.
At gunpoint, my top choice for you is NYU Stern.
(Oh, and I'm sorry to say, but HBS can probably be ruled out now. Harvard has been skewing young for several years and while you still fall within the age range of students that will be admitted, you are well outside the sweet spot.)
Love to help you get all of this sorted out and then put together some bang-up applications. PM me if you are interested in doing a consultation.
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