Hoxton and Shoreditch remain my favorite parts of town to stay in (early work bias), though in recent years I've mainly stayed around Tower Bridge. Perhaps an obvious statement, but London is very large, and jumping from site to site
With the right train, most of Kent is accessible for weekend getaways from London. We had a wet, cold, and reasonably pleasant December trip covering Canterbury, Rochester, and a bit of Gravesend. Canterbury Canterbury is a UNESCO World Heritage Site and a
Bath is lovely, an easily accessible getaway from London, known for and named after its Roman-built baths - as well as Jane Austen, and more recently, Bridgerton filming sites. I had a half day adventure from London with Alex in 2016