Heathrow layover

You may have 13 hours between flights, but after clearing passport control and leaving the airport and arriving in Windsor (or London); then returning to the airport and arriving there 3 hours before your next flight, you will only have about 7 hours of usable sight seeing time.
That's plenty of time to tour Windsor castle (if it's open) and the town, see Eton, and have lunch, and maybe tea. Or you could take the Tube into London and see a few of the sights. Perhaps walk around the Buckingham Palace/Westminster areas, up to Trafalger Square. Lots of places around there for a meal.

Remember that you will need to go through UK Border Control when you arrive and as you are leaving the airport - this can take time. The Thames Valley no. 5 bus will get you to Windsor in about 20 minutes leaves from the Terminal 5 bus station or the Central Bus Terminal near Terminal 3. Remember you need to be back at Heathrow three hours prior to departure. Be aware it gets dark early in January.

Windsor is a good layover option for whatever weather you find when you land. The Castle is the main attraction along with St George’s Chapel. Nice walks along the River Thames if the weather is decent. Think about grabbing a shower to freshen up before you leave the Airport (see the Heathrow website for info on that and storing luggage), it will freshen you up for your day (assuming an overnight flight).

Another option could be Richmond and Kew Gardens. Richmond takes about 30 mins by Tube.

3 hours for international long haul flights, a couple or 90 minutes (depending) for domestic and short haul

is your layover on the way home or on the way to another European destination? Same terminal at Heathrow? Same ticket?

The Thames Valley no. 5 bus will get you to Windsor in about 20 minutes leaves from the Terminal 5 bus station or the Central Bus Terminal near Terminal 3.

The #5 goes to Slough direct from Heathrow- not via Windsor.

You want the First Berkshire bus #8 from Terminal 5 (only, not Central Bus Station) every 30 minutes or the faster Thames Valley #703- https://passenger-line-assets.s3.eu-west-1.amazonaws.com/courtney/CTNY/703-timetable-20240325-147590d9.pdf
That is a 24/7 service (also half hourly), and is also from Terminal 5 only.

So 4 buses an hour.

From other Terminals to T5 use the free landside train facility on Tube/Heathrow Express/Elizabeth Line.

It is a tough call, but I would not risk trying to get to central London for such a short amount of time - you never know whether the Piccadilly Line will be instituting "replacement bus service", and if in a car, traffic can be brutal. Therefore, personally, I would choose Windsor. If you have never seen a typical, real South English town, and want to completely avoid other tourists, take a 423 bus to Hounslow (other buses are available). The Indian food found all over there, is amazing, although the town itself is unremarkable looking.

Should you just want to hang around near the airport, the White Horse Pub on Bath Road, Longford (very near T5) is pretty cool. Bath Road going to London on the North Side of the airport is not very interesting at all, but there are plenty of places to grab food.

As mentioned already, the border security can take a while, since the automatic gates don't work half the time, so factor in that time (you might get through in 5 minutes, you might not...). And when coming back, security can take time too, since they check absolutely EVERYTHING. Just another note, if you buy something, the VAT office is right near security/departures at T5, so you can often get reimbursed for VAT on whatever you have bought in town. Have fun!

if you buy something, the VAT office is right near security/departures at T5, so you can often get reimbursed for VAT on whatever you have bought in town.

sorry, that's no longer the case. The previous Government eliminated VAT refunds for tourists.

When did they do that? I did it two years ago.