Actually, your best bet to get into central London from Heathrow is the new Elizabeth Line on the tube. A similar amount of time as the Heathrow Express, but with many very convenient stops. No need to buy tickets, just tap in and tap out with a contactless card in both directions. If you want to see some specific things, you can just take a regular bus (also tap in but no need to tap out) and sit upstairs. Here's a good bus map for central London: https://content.tfl.gov.uk/bus-route-maps/key-bus-routes-in-central-london.pdf

Alternatively, just go into London, choose a picturesque area, have a nice meal and a pint at a pub, and walk around a little. It would break up the trip! The Tottenham Court Road stop would be a good one for this--not too far from Covent Garden, Soho and the British Museum.