Can you register a car in a different city?

In most states in the US you can register a car at any state Department of Motor Vehicles (or equivalent) office. Some states require that you register it in your county of residence (generally to ensure that the proper county taxes are paid on it).

Some cities have a personal property or excise tax that's due on vehicles. If you live in such a city, you'll almost certainly have to pay that and pick up the city sticker in that city. Registering a car in a different location to avoid paying taxes on it is a form of tax evasion.