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Hi Gloria
Well if it is less than a 6 month visit you are planning, then all should be fine. But you said you wanted to move to Dover for at least a year in your original post, which would mean your first hurdle would be getting the appropriate visa from the British Embassy for staying that long. I hope you have that in hand. I would bring appropriate references with you with regard to renting a property, rather than expect a potential landlord to obtain them from so far away.
I haven't lived in Dover since around 1999, which was temporary, as I moved away (almost) permanently in the early 80's. However, I have been a regular visitor. Where in Dover you live will be dependent on what you can afford, I guess, as well as need for public transportation, closeness to stores etc. I think compared to most American towns and cities, English towns like Dover have pretty good public transportation systems with local buses and trains to Canterbury, London etc. I think you'll find a lot of people from Dover might say River (which is an area in Dover west of the main town - and yes the River Dour runs through it - hence its name) is one of the better parts of town, as is Temple Ewell which is next to River. There is a small train station at Kearsney (kind of on the border of River and Temple Ewell) where you can catch a train to Dover, Canterbury or stations up to London. Both places are residential though with just a few corner shops, so youd need to go somewhere further away for a supermarket.
One thing I have noticed on my returns to Dover is that travel to France and the continent has actually got a bit more difficult, if you're leaving form Dover, which sounds crazy as its so close. In the old days, it was easy to go as a foot passenger on the ferry, get off in Calais or Boulogne, and catch a train from the port to Paris etc. Seems like so few people travel as foot passengers now, that the transfer between all the methods of transportation is more difficult. This is partly due to the port now mostly catering to car or truck traffic, and partly due to the channel tunnel. If you are making regular trips to the continent, you might actually be better off living near a station that has a stop for the Eurostar trains from London to Paris and Brussels, but that is probably either Ashford or Ebbsfleet, which are inland from the coast. A few years ago I went to see my uncle in Brussels, travelling from Dover via ferry to Calais, bus to the Calais train station, train to Lille, and then the Eurostar train to Brussels. A nice adventure but took about 8 hours. If I'd gone by train from Dover to Ebbsfleet or London (going in the wrong direction, effectively!), and then the Eurostar to Brussels, it probably would have taken about 4 hours.
Let me know if you have any questions, although I am sure people that still live in Dover can give better advice on places to live and other day to day living advice.
Cheers.