I don't want to have anything above my new granite other than the faucet. I need info on how to take care of the overflow vent that is usually mounted on the sink. My sink is an undermount. Thanks for any help.
Take alook at these, they're made for just such an application
I assume that you're talking about the air gap for the dishwasher. They are a code requirement in many places. If they are required in your area, you're pretty much stuck with it, though it could be disguised. There are several devices sold that combine the air gap with a soap dispenser, Dixie Cup dispenser, etc.
The reason an air gap is required by code is that it provides an outlet for dirty water backing up due to a clogged drain.
Otherwise the (sewage) water could back up into the dishwasher and that could make you and your family sick.
Here in California they are required.
Blanco makes some that are decidedly un-airgap-looking.
Or you can go for one of the combo units as your other commenter suggested.
I have not seen those before so I can't say from experience that they work well as a soap dispenser; but they certainly look viable.
Air Gap combo units