I think you should run your startup wherever you feel comfortable living.
My city is a great city, it has many neighborhoods you can feel "home" in, it has great food, it has a lot of money flowing through various veins. The startup community here is varied, focussing on a variety of business opportunities, and not necessarily totally digital. There’s a certain sense of underdog vs. the world, which reflects a certain reality of startup exits, but also is a bit ridiculous given the scale of opportunities here.
My city has many detractors, who will tell you there's high crime, questionable people riding the subway who will harass you or worse. The money may well be coursing through its veins but it’s difficult to get access to it. Real Estate is expensive. VCs are unrealistic about valuations and business opportunities and exits. It’s incredibly difficult to hire designers and developers who are exploiting the tight market to their benefit and employers’ detriment.
The scenery and lifestyle in my city is fantastic, great vistas, many opportunities to run, hike, bike, swim, kayak. You’re a couple of hours’ drive from various ski & snowboarding areas. And you can just as easily surf if you wanted to.
Now, this comment could apply just as equally to SF as to New York. Each has its drawbacks and its fantastic benefits. Fanboys will argue until there are no more karma points to be awarded over which is the “best” city to be based in.
I think that if you’re really that ambivalent about where to be based, spend a month in either city and a month in some random city (say, Pittsburgh, or Austin, or Boulder). Because it’s clearly neither technology, nor access to customers, nor access to money that’s going to drive your decision, it’s how it feels to live there and whether you will feel at home there.
I don't think you can do wrong by coming to NYC, but I also don't think you'll necessarily do better here than in SF or Pittsburgh or Austin or wherever.
Assume your startup fails entirely: where do you want to end up living? NYC is great, but you'll definitely burn through cash faster here (or in SF) than in a cheaper city. SF has a lot going for it, but will you really be there or in the Valley?
Rather than ask people to justify why one city or another is better, why not list the criteria you're using to make your decision?