Start with Winchester. It’s just outside of London, easy enough to drive/train/coach. Really beautiful historic city, with a cathedral, The Great Hall, a 1000 year old pub. Good range of shops, some nice boutique places, bunch of decent restaurants and other eateries. It’s also really walkable as a city, can take a wander up St Catherine’s Hill, start the South Downs Way or any of the other many trails about. Should be a good jumping off point for your exploration.