I presume you are aware that football fixtures are regularly changed to fit in with the tv coverage? A weekend match can be played anytime between Friday evening and Monday evening. The precise date and time is confirmed 2 or 3 weeks out. The new football ground is quite a way out of Brighton. Parking is difficult there, so allow plenty of time if you opt for a park and ride option. It will be dark around 4.30pm, so when you come out of the match.
How many nights do you have between Brighton and Canterbury?
You should be out of Heathrow by 10am, hopefully. Renting a car after a long flight for the (possibly 2 hour) journey to Brighton isn’t a good idea with jet lag.
Lewes is easily covered from Brighton. After your time in Brighton, you could head to Rye. If you want somewhere twee inland, consider Burwash, Robertsbridge or Bodiam (good for several National Trust properties including Batemans and Bodiam Castle, both of which are still open in November).
There is a choice of several castles if these are of interest - Leeds, Hever, Walmer, Deal or Dover. Dover itself is a dump, but the castle is worth a visit - stay in Hythe, Sandwich or Deal. The gardens won’t be at their best in November and many will have closed for the winter.
Dungeness is unique and worth seeing for its collection of unusual houses (eg one made from a former railway carriage) and to climb its lighthouse. I don’t think the steam railway runs in November.
I would miss the section of coastline between Sandwich and Herne Bay, as it’s not the prettiest. Whitstable has some good seafood restaurants and is a good base from which to see Faversham and Canterbury.
There maybe local events happening in November that maybe of interest, but the dates for many of these are not yet available.
Shoeburyness and Southend aren’t close to where you are going to be as they are a 2+ hour drive from Canterbury. Personally, I would not recommend either.