It makes sense to rent a car if you plan to see not only Prague. There are many interesting places in the Czech Republic. It’s no worse in other cities. And there are fewer tourists.
Rent a car without a driver: Localrent.com, Rentalcars, Economybookings or Discovercars. You can rent a car with a driver through Gotrip24.com.
Might come in handy: car rental instructions | article about transfers in the Czechia.