Where would one deploy deep space atomic clocks?
In practically any vehicle that goes beyond Earth orbit.
The press releases imply that these Deep Space Atomic Clocks will form the basis of a solar-system wide equivalent of GPS. While that might be the eventual outcome, that is not the immediate advantage. The immediate advantage is that this technology will effectively increase the capacity of NASA's Deep Space Network by a significant amount.
Currently the DSN determines the range and range rate to a spacecraft using two DSN antennae. One broadcasts a signal to the spacecraft, the other receives a signal from the spacecraft. In between, the spacecraft receives the signal sent by the outgoing DSN antenna and sends it right back to the receiving DSN antenna. This two-way ranging provides the extremely precise range and range rate measurements that are needed to estimate where the spacecraft is/was. The spacecraft's state can be determined only after collecting a number of such measurements. The downside: This takes two DSN antennae.
There is a one-way ranging alternative that only requires one DSN antenna. If the time tag on a signal from a spacecraft can be trusted, the difference between the time tag on when a message from the spacecraft was sent and the time tag on when the message was received on Earth yields the range to the satellite. That however requires an extremely stable spacecraft clock, much more stable than the best crystal oscillators can provide. The Deep Space Atomic Clocks should be more than accurate / stable enough to enable this one-way ranging.
In the future, spacecraft that communicate with one another might be able to bypass the need for communicating with the Earth. But that's science fiction future, at least for now. The realistic future is that this technology will make the DSN much more efficient.