1 day in London before going on a cruise.

London is a huge and amazing city. Do you fly in, have the rest of that day and leave the next day for your cruise? Or do you actually have the day you arrive plus the whole of the next day before leaving on your cruise after spending 2 nights in London? That makes a difference of what suggestions we can offer you and the best location to stay in. Of course, first thing you must do is buy a guidebook, I suggest Rick Steves :-) and start browsing through it. Get back to us on how much time you really have so we can make start giving you ideas.

Heathrow or Gatwick?
One night or 2 nights?
Southhampton or Dover?

are you sailing from Tilbury or somewhere on the coast? What time of year?

We arrive in Heathrow @ 10 AM on May 11, and cruise out of Southampton on May 13. I'm leaning towards the Double Tree, but trying to decide which one, but I'm open to suggestions. Would like to stay where we can walk to restaurants, pubs and sights. Thanks so much sharing your experiences, I'm so excited!!

Maybe Park Plaza County Hall or Park Plaza Westminster Bridge if you are planning to take the train from Waterloo to Southampton on May 13. A short walk over Westminster Bridge to Parliament and Westminster Abbey and then on to Buckingham Palace.
Try to get to St Paul's and the Tower on May 12. Enjoy.

Premiere Inn Waterloo or Premiere Inn County Hall.

Walk across Westminster Bridge toward Big Ben.

Meander around Parliament Square, tour Westminster Abby, visit the Churchill War Rooms.

Walk up Birdcage Walk through St James Park to Buckingham Palace, then across the Mall to Green Park, through Green Park and down Piccadilly into SOHO. From there onto Leicester Square then down Charing Cross Road to Trafalgar Square.

Have a coffee at COSTA and walk down Northumberland toward the river past the nice hotels and The Playhouse theatre.

Can either cross the bridge heading back to your hotel or walk along the Thames path back to Westminster Bridge.

Nice LONG walk that will provide an excellent POV of London's must sees.

Use the Google Satellite view to plot this route.

You should definitely get a guidebook. London has, as you say, so many possibilities, and trying to figure it out from the internet is (as another poster here likes to say) trying to take a sip from a firehose.

Which Rick Steves book will be best will depend on where your cruise is. If it's to the Baltic Sea area (Copenhagen, Stockholm. St. Petersburg), definitely get Rick Steves Northern Europe Cruise Ports: https://store.ricksteves.com/shop/p/northern-european-cruise-ports. This book covers London and Southampton, as well as all (or nearly all) of the ports you will visit. If your cruise is the Norwegian coast, it only has some of your ports, but may still be useful (go to the link and open "What's Included" to see how much of your cruise it covers).

However, if you're going on a British Isles cruise, get his Pocket London guide, as this is specifically designed for those on a short visit: https://store.ricksteves.com/shop/p/pocket-london

I think you can actually get a nice taste of London in one long day. Agree with previous post to start at the London Eye, walk past Parliament, visit Westminster Abbey, and then walk to Trafalgar Square. (LOTS of stuff to see between Westminster and Trafalger.) Then finish up at St. Paul's Cathedral.

You could spend a lifetime exploring London, but you can get a fun sample in just one day.