Anything will do. It's hard to say what you'd be happy with. I happen to like road bikes best. My main commuter bike currently is a Bianchi Volpe which could be a called a cyclocross bike, but not really, since it's way too heavy. Normally, I prefer to be semi-upright in the city, but the fit is so good that I'm very happy with the drop bars. I have 32mm tires on it. Any bike can take the beating that the city will dish out. That's not the question. One question is what you'll be comfortable on. Performance is another thing. Slow bikes punish you for exerting yourself too hard, and this is why I'm glad you're hoping to skip hybrids. I'm not a fan of those bikes. So I'd say your instinct to look into cyclocross bikes is a good one, at least to my taste. And taste is a big factor in deciding which style of bike you choose.