London few days post cruise--where to stay?

Look on Booking.com, they show a wide range of lodging options, from hostels, to small hotels, to chains, to apartments. Also look at other chain hotels, Premier Inns is popular for London, decent locations, decent prices. Ibis and Holiday Inn are also good options. If you want a bit more luxury, there are lots of options, but London is definitely a "high cost" town.

As for location, London is a huge area and the sights are spread out a bit. The best advice is to stay somewhere on a major Underground line. Lots on here like the Kensington area, the Kings Cross Station/Bloomsbury area seems to be popular, I have stayed in the Southwark area, Victoria Station area, Hammersmith, and Camden Area. The key, like I said, is have a good tube stop nearby.

Added: As for length of stay, depends on your interests, but there is lots to see. Many museums (most free), the churches, the Tower of London, Markets, neat neighborhoods. Whatever you decide, three days, four days, two weeks, there will be more than you can see, you will need to pare down a list regardless.

It's worth considering areas close to where you will come into and out of London. From Southampton the trains come into Waterloo. If you're flying out of LHR then the tube from Westminster right across the river from Waterloo would make a lot of sense.
If you're in the rough budget for the Grosvenor then you might want to consider the Marriott County Hall. Right next to Waterloo and with a perfect view of Parliament across the river. If you want to be cheaper then there is also a Premier Inn in the old County Hall and another by Waterloo. All 3 very central locations right by the river.

I do not recommend using Air BnB for London accommodations. I do use them for other areas, in the US, Switzerland, and Italy for example. But in London, these owner-direct rentals can present risks, pitfalls, and uncertainty. Also, the Londoners do not like having potential housing for working people turned into vacation rentals for foreigners. This is not unique to London—other big cities (Paris, Barcelona, etc.) have such problems, and have either banned or restricted them.

But there is an excellent alternative, known as “Aparthotels” or “serviced apartments”. These offer hotel-like services such as a lobby and reception desk, professional staff onsite, and more, sometimes including amenities such as workout rooms, meeting rooms, etc. The apartments range from studios to 2 or even 3 bedrooms, all with equipped kitchens and much more space than a hotel room.

There are a number of “chains” or groups offering nice serviced apartments in London: Citadines, Locke Living, StayCity/Wilde, Marlin Apartments, Native, Cheval Collection, and more. Very few will offer 3-bedroom apartments, but your group could have 2 apartments in the same building, possibly on the same floor.

I am going to tempt you with an option from the last-named Cheval group, as friends to whom I have recommended them have been very pleased. Note that right now, as a bonus, they are offering 4 nights for the price of three (but beware, that may be a non-refundable rate).

This one is near Gloucester Park, in South Kensington.

https://www.chevalcollection.com/cheval-gloucester-park/

Cheval has other London locations as well but I did not check the others for 3-bedroom units.

I am sure you will get lots more recommendations from others, and hopefully they will be options with 3- bedroom apartments, as not many serviced apartment companies offer them. The ones that do exist tend to get booked up early, but the Cheval Gloucester Park apartment is available for a 4-night stay on the random September dates that I checked.

Just a heads up that another way to travel from Southampton to London is by National Express Coach. You would arrive at Victoria Station if you go that route.

My favorite hotel is Premier Inn Waterloo or Premier Inn County Hall which is just a few blocks away. Not fancy, but good value.

Tricia,
Lots of lodging options in London but as Paul already mentioned, try to stay relatively close to a tube station. You will most likely use the tube to get around, it is very convenient but since most of you are first time visitors in your 60s be aware that there are often steps although many escalators and some elevators. Also I like to take busses as I can see more. The Transport for London website (TFL) has a very helpful route planner. I use it all the time when I am in London to see what my tube, bus or rail options are. Here is the link TFL Journey Planner You asked whether to stay 3 or 4 nights - I strongly suggest 4 nights as that gives you three full days, 3 nights only gives you 2 full days and there is so much to see and do in London, I would suggest that you add on another day or two if possible. Prioritize what you want to see and try to organize your stops by areas of the city. Also decide if you want to take one of your days to go to Greenwich, Windsor or Hampton Court, all worthwhile visits.

Thank you all so very much for ll the helpful information and tips!! Let the planning commence. I was leaning towards 4 days, but one person said why not 3--now I have an answer!!

Also I like to take busses as I can see more.

I like the buses as well, especially if you can get on early in the route and snag the front seats on the upper deck. However, you do need to consider the time of day and traffic conditions, or your cheap sightseeing tour becomes a stationary platform. I probably would not take a bus if I planned on being someplace at a specific time (I found out trying to get to a meeting!), but it is great for a leisurely ride.

The other thing about transport is payment. London has moved to a great system where each of you can just use your phone (Google/Apple Pay) or credit card to tap in and out of the tube (tap in only on the bus) and it will apply the charge and cap out the fare daily if you make over 3-4 trips. Very easy and convenient. Details here: https://tfl.gov.uk/fares/how-to-pay-and-where-to-buy-tickets-and-oyster/pay-as-you-go/contactless-and-mobile-pay-as-you-go