So, you go to work in the morning, the hot water in the pipes between the tank and sink cools off. The valve opens, fills the pipes with more hot water. An hour later, when THAT water is cold, it opens again to run MORE hot water.
There are actually two ways to do what you are describing, although the convection method only works with large vertical distances and larger pipes. You can have your house plumbed in such a way that the hot water system actually runs in a complete loop back to the hot water tank, with a very small pump that keeps hot water circulating through the entire system at all times. You will save water, and have hot water instantly at all times, but it costs in pump energy and lost heat in the pipes that weren't designed to keep hot water hot.
With your system, yes, you will save WATER at the sink, but you will not save HEAT. Over all, you will spend MORE money heating the water, running and buying and installing the pump, than you will save in water costs.
If you are really serious about pursuing this, which I don't really recommend for the above reasons, check out your local plumbing supply houses (the ones the plumbers go to, they don't shop at home depot for this stuff.) Keller Supply is a big one in our area, but I don't remember if they are national or not.