Recommendations for caching with overnight layover at LHR

[+NYPaddleCacher]

I have an overnight layover at LHR on June 12th and want to get out and find a few caches while I am there.  I'm arriving at LHR at around 1930 after traveling all day (from Nairobi, Kenya) so I'll just want to get a hotel and then do some geocaching before I have to head back to LHR for my flight home at 1730 on the 13th.  I was thinking of getting a hotel somewhere along the Piccadilly line and figured I could get up in the morning,  take the underground to someplace more interesting to do some geocaching and then take it again back to the airport.  I've seen that the closer one gets to central London the hotel prices go up significantly.  Since I'm just going to be staying one night I want to keep those hotel prices at a minimum.   I had first just thought of finding some place near the airport and doing some geocaching nearby but am considering some alternatives.   If I, for example, stay in a hotel in the Earls Court area I can still find a reasonable priced hotel and spend less time in the underground the next day, even if I go into central London.  I've never been to London before and although my trip will be brief I'd welcome the opportunity to see some interesting spots while at the same time, finding a few geocaches.  I've found geocaches in 13 European countries previously but this will be the first opportunity to finds a few in the UK.  If anyone has any suggestions given my arrival and departure times at LHR I've love to hear them.

[+JimJinks]

From Earls Court take District or Circle to Westminster (Big Ben and Houses of Parliament). Few caches around that area incl a few EarthCaches. Walk up Whitehall to Trafalgar Square where there is a new virtual and some others around there.  Under Admiralty Arch up the Mall to Buckingham Palace. Note that there are no caches hidden in the Royal Parks for security reasons. From Buckingham Palace it's then not far to Marble Arch and Oxford Street. A few suggestions I hope you find useful, enjoy London. 

[+NYPaddleCacher]

23 hours ago, JimJinks said:

From Earls Court take District or Circle to Westminster (Big Ben and Houses of Parliament). Few caches around that area incl a few EarthCaches. Walk up Whitehall to Trafalgar Square where there is a new virtual and some others around there.  Under Admiralty Arch up the Mall to Buckingham Palace. Note that there are no caches hidden in the Royal Parks for security reasons. From Buckingham Palace it's then not far to Marble Arch and Oxford Street. A few suggestions I hope you find useful, enjoy London. 

Thanks for the response.  That helped me choose a hotel I'll be staying in. I had considered a couple of other areas but found a good place close to the tube in Earls Court that will give me good access to the PIccidilly and DIstrict lines.  I'd like to spend more time in London but this stop will be after 10 days in Kenya.