Local dedicated hosting space (own hardware)

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).

What you are looking for is a Colocation facility. They are all over the place, I would just search google for one near you. Most facilities rent as little as 1/8 of a rack.

The price is going to vary depending on how much space you rent, as well as what additional services you need.

Edit
Missed that you where looking in the NYC area. We use Peer 1's Colocation facilities in the Financial district for the SO Servers

It's called colocation, search for that.