If you're going to Stonehenge, you'll probably want to continue on to the Roman Ruins in Bath as well. Since you're without a car, you may want to look into the various Guided Day trips on offer. Some of these will do Windsor Castle, Stonehenge, and Bath, which is a lot to pack into one day, but presumably doable. If you don't go with a tour and are really interested in exploring Stonehenge, Castles and Ruins, you may want to consider an Overseas Visitor's pass with English Heritage:
https://www.english-heritage.org.uk/visit/overseas-visitors/This will get you free entrance to Stonehenge, Dover Castle and a hundred or so other historical sites. There's a similar organization called National Trust, which covers a lot of smaller sites (historical houses and such):
https://www.nationaltrust.org.uk/Even if you don't join these organizations, the websites have some pretty good maps and descriptions of the various sites.
When I visited London, I got the London Pass:
https://www.londonpass.com/I'd give it a mixed review. It does give you free access to a lot of sites and often lets you skip the lines, but if you like to spend much time at any one place, you'll be hard pressed to visit enough sites to get your money's worth. On the other hand, since you get "free" entry, it does give you the freedom to take a quick gander at a site you might not otherwise have been willing to pay for. Do your homework, some of the listed attractions (eg. the British Museum) are already free, so make sure you don't use the pass for those, when you could be visiting someplace you would have had to pay for.
As for Transportation around London, you'll want to get an "Oyster Card", which you can load up to pay for trips on the metro.
Another relatively easy day-trip from London, is to head Northeast to Cambridge, Ely (large Cathedral) and Bury St. Edmunds (ruins of one of the most important abbeys in England prior to Henry VIII and location of the agreement of the Charter of Liberties, a precursor to the Magna Carta). Though that area is likely more pleasant in Summer, when you can go punting around Cambridge.
I agree with others that Edinburgh would be a great choice for your second destination, quite a bit to see and do in the city itself. Stirling Castle would be a nice day trip, if you can cram it in, but you might just want to stick to Edinburgh. Keep in mind that you are pretty far north, so in November, the days will be short.
One last tip, you may want to look into the "Rick Steves" app. He has a collection of narrated walking tours for various European Cities, including Edinburgh that are downloadable for free.
Have fun!