1 full day London....Where to stay?

Would be smarter to ask this question on the London Forum. You’ll get more responses.

Also use the search engine and type in London Accomodations.

There is nothing of interest by Heathrow and it's a 45-60 minute tube ride to anything interesting in London. I'd pick a Premier Inn that's near the Piccadilly line which can take you to and from Heathrow without the need to change. Premier Inn is a so-called budget chain in the UK, I'd say they're equivalent to maybe a Courtyard Marriott in the USA, although some of them don't feature the latest in television technology. However, you're not there to watch TV.

Earl's court might be a good location, it's a bit closer to Heathrow but still convenient enough to see London. If you're a Doctor Who fan, or just want a quick selfie, there's a TARDIS at Earl Court tube station.

You only have one day so what do you want to do? What do you want to see? I assume you’ve done some reading/research. If not, read RS book on London. Pick 2 maybe 3 things you want to do, get a map, then locate yourself near those, or close and on a tube line. No sense staying far away to save $50 and spend your very few hours in transit.

We just did one day in London last October, and we were able to see quite a bit. We rented a VRBO just a few blocks from the Tower Bridge (on the North side). Very walkable, and the taxi rides were also short & cheap. We managed to go on the Eye, visit Westminster, walked up to Buckingham, and then short taxi to the National Gallery - all in a day. Plus still had time for a couple of really nice meals in some local pubs. Oh, and we did a quick loop on the BigBus Tour. It was a bit of a long drive in the taxi from the airport to the apartment, though. In retrospect, taking the train would have been both cheaper & quicker!

How late are you arriving on the 19th, and how early on the 21st is your departure flight? Those times might factor into getting a room in London itself or staying near the airport and journeying into London early on the 20th for the day.

They have a London Express fast train that goes to Paddington Station. Just south of there are the Bayswater and Queensway underground stations with Kensington Palace and Hyde Park close by. The neighborhood is pretty yuppie with decent restsurants, etc. It is a straight shot into Bond St. and the best shopping. The underground can get you around quickly from that area.

Because of transportation considerations to Heathrow, I would suggest Paddington for this short stay.

Try travelodge (they are not on comprison sites) they are cheap rooms and always clean. They have many locations throughout London Euston is a good one as you are close to the British museum and a tube line.