The Premier Inn Dover Central (East Ferry Terminal) is about a 10 minute taxi ride to the Cruise Terminal. The front desk staff here were behind helpful, including pre-booking a taxi for us. They held out luggage as well on the cruise morning. Our main reason for staying here the night before our cruise was to be able to walk to Dover Castle. It was an easy 10-15 minute walk from the hotel, and we were trying to see the castle before we set sail on our cruise.
The rooms are very small, very basic, and do not include Air Conditioning. (It's not usually that hot there apparently). They did include a small in room fan. If you have traveled to Asian, the rooms were bigger then a standard Japanese hotel room, but only by a bit. Think NYC room size, with a smaller bed. The beds are close to an American Queen size.
If we just needed a place to sleep the night before a cruise I wouldn't hesitate to book it again.
There are two other Premier Inn's in Dover, I haven't stayed at either of those, and both were further from Dover Castle and the Cruise Terminal so we ruled them out.