Where to stay in London- 3 adults

London sites are pretty spread out. Budget is also important to know. If you know which sites you are focusing on then stay near those. If you are going all over then stay close to a tube station.

Even better: Stay close to a tube station served by two lines. That increases the number of places you can reach without taking the time to transfer. Your trip is very short for a city with all that London has to offer; make efficient choices.

Three nights is not very much time to see one of the world's largest cities, so you'll have to prioritize which locations you most want to see. If you find that they're clustered in a certain neighborhood, then try to book a hotel near the cluster. If they're all spread out, then -- as the previous comment suggested -- choose lodging near an Underground stop. Among the different Underground routes, the Circle line is especially useful for many of the popular tourist destinations around London.

Take a look at this small hotel about 2 blocks from St. Pancras and Kings Cross Stations. trains and many metro lines.

The Jesmond Dene on Argyle St.

I've stayed here several times - it is more like a B&B - Full English Breakfast is also available.
If you pay your bill in cash, they do give you a discount. I know there are triple rooms ( and a quad on the 4th floor.)
Jesmond Dene Hotel

At the moment your question is impossibly general. You may be limited if you want to share a room - triple rooms are rare, and so are American-style rooms with two double beds. Rooms tend to be small, a/c isn’t standard, some small hotels won’t have lifts (elevators).

Some questions for you...

What have you looked at so far and why have you rejected them?
One room or two?
Cost per night?
If a hotel, would you prefer clean, crisp modern chain hotel or slightly tired old character property or fancy pants expensive full-service hotel?
Which attractions are you most hoping to see?
Is a/c important to you or do you prefer the British approach of flinging the windows open?

Premier Inn, County Hall - pretty good location, especially for walking, IMO. Plus, depending on how you book, you can cancel later if you find something else you prefer. I have stayed there 3-4 times.

The London Elizabeth Hotel is great, two minute walk from Lancaster Gate Tube Station, across the street from Hyde Park/Kensington Palace and around the corner from a great pub The Swan.