St Albans
Vying with Colchester (sadly also very run down these days) for England’s oldest town/city, St Alban’s is north of London, not so far out. It’s on Thameslink, so any station on that line with maybe a change.
The cathedral is genuinely old.
Also, there is a small railway to and from Watford, so you could incorporate a trip to the Harry Potter thing.
Honourable mentions
Windsor (for the park)
Colchester (for the castle)
Whitstable (for the seafood)
Rye (for nice pubs)