The Chef's Table sounds like a great idea. I hadn't realized that they put different parties together for that. Of course, it does bump up the cost, but it could wind up a great experience as a solo. It's great to engage in dinner conversation during a solo trip (I travel a lot for business, and often wind up on my own for many meals, and I always enjoy the occasional conversation that happens with fellow diners).
I always feel more conspicuous sitting at a table and reading--not that I think anything is wrong with doing it. So, I usually just sit, think, and often egregiously eavesdrop on fellow diners. I know, it's a bad habit. But, there's little else to do...