Can I drive and operate an Uber in multiple cities/states/territories?
The Guru Take
You can drop off your passengers anywhere. You cannot pick up anywhere, however.
Uber drivers can only operate and pick up passengers in areas for which they have been assigned and approved. This has to do with how each local areas have different laws and regulations. You are applying to drive in a certain territory, and you are approved for that specific territory.
To clarify, it is important to point out that you can pick up in your own area only, but you can drop off outside of your territory in any location. This means that you can leave your territory with a passenger but you cannot pick up on the way home.
Uber can make exceptions to this rule and approve you to drive in multiple states if given a proper justification. They also approve temporary relocations, where, say, you decide to move to another state for the summer, they can grant you to operate in that area for a few months.
Lyft used to have a much relaxed policy, where you could drive in multiple cities and states, and they did not have the concept of having any territories. However, as the local laws and regulations tightened, they have implemented these restrictions.
UPDATE: It is important to also remember that depending on your local area, Uber often extends your coverage area (where you can pickup and receive requests from) to the surrounding territories/states. For example, if you are approved to drive in New Jersey, you will receive requests in states like PA, NY, DE, CT, and Western MA. (not NYC, due to TLC requirements.))