My bus from Whitechapel into town always gives me a lovely view of St. Paul's - day or night, sunshine or rain, it's always different and special. A few times I got off just to marvel at it from the outside (as I haven't managed to swallow the huge admittance fee nor turn up during mass just to look around) and wander the area.
Nearby is Bea's which I'd read does an excellent banana bread (true) but I discovered also does the only chai latte in town that remotely resembles the type I like in Melbourne.
On my visit, it tended to be older people enjoying cakes and tea but whatever the preference it is a great daytime break.