Long layover in Heathrow

I would suggest going to Windsor, it’s only a 15 minute cab ride from Heathrow. You could tour Windsor Castle, have lunch in one of the pubs, walk to Windsor Great Park it’s a five minute walk from the castle.

What time of day do you arrive?

Arrival in Heathrow is 5:30 a.m.

05:30 + 13 hours = 18:30.
You should be completed with immigration and exit arrivials by 07:30 latest. 2 hour check-in = bacxk at terminal by 16:30, possibly earlier if it is an intercontinental flight.
Perfect timing. Taxi to Windsor, get some breakfast, tour the castle and the rest of the town (+Eton). Taxi back to terminal.

You could go into central London. In that case best to have a definate destination. My suggestion: South Bank Walk
Tube to Tower Hill station (buy Oyster Card at Heathrow). Walk past the Tower across Tower Bridge to the South Bank. Walk along the South Bank all the way to Westminster. Walk back across Westminster Bridge. Then tube from Westminster staion back to Heathrow,.

See this webpage describing the walk: https://en.wikivoyage.org/wiki/London_South_Bank_Walk
Google "South Bank Walk" for other descriptions and videos.

A few years ago I had a similar situation. I went into London to the British Museum.

If you decide to go into central London, take the Heathrow Express. It's only about 15 minutes to the city whereas driving could take an hour or more.

Windsor is charming!

If you decide to go into central London, take the Heathrow Express. It's only about 15 minutes to the city whereas driving could take an hour or more.

Nobody would ever suggest driving into central London.
The options main are Heathrow Express to Paddington, or the tube. Heathrow Express is faster, but Paddington is only on the edge of central London. Unless you are heading for a hotel near Paddington (which you aren't), you still need transport (tube) to your final destination.
It is a lot cheaper, and for most of central London it is simpler and just as fast, to take the tube all the way from Heathrow to your final destinations.

Other options are coach (bus). Cheapest, slow and only gets you to Victoria coach station. "Last mile" transport still needed.
Pre-booked taxi, aka mini-cab. middle-price. No faster than the tube, depending on time of day may be slower.
Taxi from taxi-rank. Most expensive option. No faster than the tube, depending on time of day may be slower.

Thank you all!