] Not an abbey, but what about Berkeley castle? Still inhabited and formerly a royal castle, there was also the famous Dr Jenner living in the village...

JA's GGGG grandmother was Catherine Berkeley and Catherine Berkeley's sister, Elizabeth was JA's GGGGGG Grandmother.

Catherine's descendants who were JA's ancestors came to own Stoneleigh Abbey (The Leighs).

Elizabeth's descendants who were JA's ancestors came to own Cannons and were the Dukes of Chandos.

I wonder if JA ever visited Berkeley Castle in the manner of E. Bennet and her aunt visiting Pemberley?