If you are in the area with time to kill, avoid Petticoat Lane market. It’s not worth the effort. Avoid Dirty Dick’s.
Spitalfields is better, if you like that kind of thing, rather touristy but real history and some good eating places.
Better still, take a 10 minute walk, past Moorgate, to the Barbican Arts Centre. See a world class concert or play, have a cocktail and admire the architecture.
There are some nice art galleries in the area, though we say avoid Brick Lane as it has a bad reputation.