Husband and I making first trip to London ( en route to conference in Manchester) in late June. We will be there for 4 days and 4 nights. We like to explore the soul and history of a city while enjoying only the "must see" tourist attractions (obviously Buckingham Palace). We always like to see modern art and arts venues. And we want to see at least one castle while in the country (neither of us have ever seen a real castle). Seeking recommendations on what neighborhood to stay in and any specific soulful sights, hangouts, historic and/or arts districts. We don't mind lots of walking.