Where can I find local dedicated hosting space for my own hardware?

I know I can rent dedicated hosting from various companies online, but usually I think that means I'm renting their hardware too. I just need a space with a network connection and a power outlet. That's it. How much would this cost? What would I search for? Is it available easily? Or would it only be the sort of thing huge companies would do? I'm in the greater NYC area.

It's for a project I'm working on, but the thing's loud and annoying. I'd be willing to pay a little to get it out of sight and out of mind. I don't even care too much about the quality of the network connection. I'd rather not rent other people's hardware cause it probably would cost a fortune to rent a machine like this (tons of ram).