Where to split existing water pipes for new pipe run?
If all the plumbing in the image is 3/4", then I'd simply tee off as near the new faucet as practical. In the drawing, somewhere between the laundry and the kitchen.



If you're worried about losing pressure to the other fixtures when the faucet is on, then you'll want to tee off using a 3/4" x 3/4" x 1/2" tee. 



That way you'll have 3/4" all the way to the kitchen, but the supplies to the new faucet will only be 1/2".  This configuration will help maintain pressure to the kitchen, when water is being drawn from the new faucet.

You'll want to install "anti-siphon frost-proof sillcocks".



These have a vacuum breaker built in, so water won't be pushed back into the plumbing. Without this feature, you could potentially contaminate the water supply. This is required by code in some areas.  

The frost-proof feature should prevent the plumbing from freezing during the winter. The sillcock has a long stem, so the water is actually shut off way back where it connects to the plumbing, instead of right at the spigot. This means that when the valve is closed, there should be no water in the entire assembly.  Basically, the water is shut off back inside the warm house, instead of outside where it's cold. NOTE: If you have a hose attached to the spigot, make sure the hose drains after each use during the winter.