Disembarking from cruise ship in Dover, London

Is there a reason why you selected that particular area to stay?

No. It was just a random choice. Any suggestions would be great. To add, we will be flying to Dublin the next day to spend a week before flying back to U.S.

I think we need a little bit more information from you. Are you willing to take trains/public transportation or are you asking about a private driver?

You could take the Carnival transfer from the ship to Victoria Coach Station ($440) for 4 people and then take a taxi from there to your lodging.
You could take a taxi to the train station in Dover ($10) and then the train to Victoria Station ($272) for four people and then a taxi from there to your lodging.
You could taxi to the coach station in Dover ($10) and then take a National Express Coach from there to Victoria Coach Station ($40) for 4 people and then take a taxi to your lodging. (takes roughly twice as long as train)
Private Driver arranged through Get your Guide, $459 for 4 people.

You can see of all the options, the Carnival transfer is the worst.

I read your note that was written while I was writing my last post. So, you really aren't thinking of seeing much of London, it is just a stop on the way to Dublin. Is this correct? Which airport are you flying out of? In your case, I would pick lodging near Paddington Station if going to Heathrow the next day. It is an easy transit on the Heathrow Express (buy in advance for best pricing) from Paddington. Premier Inn Paddington Station is directly across the street from the station and offers reasonably priced rooms.

Carol NR has given your options for getting into London. As for your accommodations, I'd look for a place with easy transport to which ever of the London airports you will need for your flight the next day. If you tell us which airport, we may be able to suggest a handier hotel location.

Dublin really is not that great, it's a shame you are skipping London.

I would get the train to St Pancras and the tube (circle line) to Shepherds Bush.

It's OK talking about National Express but there are only 4 buses a day. If you miss the morning one (0800 or 0915 on various days of the week, so very unlikely to make it disembarking a cruise unless self disembarking, and the ship isn't delayed ) it is a 4 to 5 hour wait.

Book ahead for the train on a train specific Advance Ticket so say late morning 10 to 11am, and the hourly train is around £16 ($21 US) each to St Pancras.

I'd take a taxi to Gatwick Airport, fly to Dublin, and skip London altogether, as you're spending so very little time there.

Firstly, are you aware that Dover is not in or near London. I would guess it's 70 miles away.
I prefer to stay outside central London mainly due to the price of hotels there. Shepherd's Bush Green is only 5 minutes by tube into the centre and there is a massive Westfield shopping mall there. I have stayed in a Premier Inn a mile or so away from SBG in Hammersmith which is on the Piccadilly tube line which has direct link to Heathrow airport, so handy if you are flying from there.
It's a pity you are skipping London for Dublin as there is so much more to see in London than to Dublin.

If it were me, I would get the fast train from Dover Priory to London St Pancras. Stuart is absolutely right that you should book ahead for the best price- the fares on this route can be particularly expensive as it's (currently) our only high speed rail line.

From St Pancras it's easy to get either the Circle or Hammersmith and City line to Shepherd's Bush Market. I would say this is a good place to stay, lots of restaurants etc nearby and well connected. Which airport are you flying out of?

Let's all remember that we all have personal preferences and different reasons we may want to visit different places, and someone may prefer to spend a week in Ireland (we don't even know for sure it will be Dublin specifically for the whole week) than London.

a reminder that you will be humping your luggage up and down the stairs at Shepherds Bush Market. At that place the Underground is above street level, about one and a half or two stories above the ground, the station is at a bridge. No escalators or lifts. you come out right onto the street.

The question I have, and it has been asked before, is which airport will you be flying out of?

Given the brief nature of your stay the key is to stay somewhere that is readily accessible to transport from Dover and to whichever airport you are flying out of a day later. Whichever of the 5 airports it is, Shepherd's Bush is not the answer.

We are flying from London Gatwick to Dublin. We do not expect to see much in London. We did however schedule the London Lights Night Tour. I appreciate all of your input.

I forgot to answer that we are willing to take public transportation.

From Shepherds Bush the easy way to Gatwick is the Southern train to East Croydon, hourly, then any train to Gatwick. The first weekday train is at 0619.

For Gatwick, Shepherds Bush isn't a particularly convenient location. It's doable but a bit of a schlep with luggage.
If you can change your London Accommodation booking somewhere in Victoria will be a lot easier for you.

Thanks for the additional information.

I suggest taking the train from Dover to London since you are good with public transport. It will be quick and advance tickets will not be that bad.
I agree with the previous poster that staying near Victoria station will make things much easier for you. Lots of nearby lodging choices to choose from. Look at the Premier Inn Chain. This UK chain provides a consistent product and usually good value.

You don't need to stay near Victoria to get to Gatwick easily! As Stuart says, you can get a train from Shepherd's Bush to Gatwick, you just need to change at East Croydon. There are lots of ways to get to Gatwick, including the Thameslink- really any station along the Thameslink is just as convenient as Victoria. There used to also be a direct bus from Shepherd's Bush to Gatwick but I don't believe that's run in quite some time.

Call me crazy, but doesn't it just make sense to get from the cruise port to a hotel near Gatwick airport? That is going to take nearly 3 hours, I think. I would just scrap the idea of seeing anything in London. Otherwise, isn't it about 2.5 hours from the cruise terminal to Shepherd's Bush and then an hour from Shepherd's Bush to Gatwick? That is a lot of schlepping.

It would be perfectly possible to go to a Gatwick hotel, drop your bags and then get a train into central London for your evening tour. Then an easy train back to Gatwick unencumbered by bags. Although you would probably need to seek out the train options from Dover to Gatwick which avoid going via central London.

As there is no particular reason why Shepherds Bush was chosen as a location to stay it just feels like a bit of unnecessary effort for one night when there are other more convenient locations, when both coming and going, to stay.

Dover to Gatwick you change at Tonbridge and Redhill. The price is £28.30 per person ($37 US).
Dover depart 28 past each hour, 68 minutes to Tonbridge, 25 minutes to change trains, 32 minutes to Redhill, 16 minutes to change, 8 minute ride to Gatwick.

So the 1028 from Dover arrives at Gatwick at 1257.

That is as fast as routing via London.

There are no Advance train specific Tickets on this route, so it doesn't matter what time you reach Dover station. The price is the same if you buy weeks out, or on arrival at the station.

Just my 2¢

This is our first time visiting London.

If you really want to visit London, stay more central, even if it is only for 1 night. You'll have the whole afternoon to see a bit London. You should find plenty of affordable hotels for May of next year.

We did however schedule the London Lights Night Tour.

Have you already booked this? I am surprised a legitimate tour company is already taking bookings for next May.

You may want to rethink where you are staying. Based upon what you posted, I would take the train from Dover to Victoria Station and stay at a hotel in that area. A good one is The Resident - Victoria. We have stayed there before and would again. It is centrally located for walking to the various sites. The next day take the train from Victoria Station to Gatwick.