Connect two routers via wifi?

I have a wireless router connected to my current cable modem, and it works fine. However, I would like to set up several computers in a location that is within wireless range, but where it is impractical to run ethernet cables from my current router. I could purchase PCI wireless cards for each of them, but that seams wasteful and expensive. Do routers exist that accept wireless as an input?

Something like:
Modem - wired - Router - wireless - Router - wired - Computer

To do what you propose you have to make sure the router(s) support WDS and there are other complications.

I think the adapter approach would be less problematic -- especially as most wireless routers cost about three times the price of the cheapest wireless adapter.

qzerp: you need what I would call a repeater -- a device which takes existing wireless signal and re-emits it.

I'm not sure what the correct technical term is but for simplicity's sake I'd stick with Linksys. Have a look at their site and post a query with their tech help guys or on their forum -- though it's the dumb kind where you have to buy a product before they'll let you post, a search may reveal a useful existing answer.