I saw a flat I really like off Commercial Street about a 5 minute walk from Aldgate East. I know Brick Lane has some fantastic places to eat/drink and Spitalfields is a great market. What I am unsure about is the rest of the area as you travel east on Commercial and around Henriques Street where the flat is located. The buildings all seem a bit run down and some areas seem like they would be dodgy after dark. Is it safe there?
I work at one end of commercial street and am about to move down there again, I lived in Tower Hill for a year when I first move to London. So know the area fairly well.
I would say, it depends on your definition of "safe". Have you been down there at night? Ultimately it depends on what your personal level of security is and how you feel.
London is a strange beast, one street can be fine, you can move two streets over and it can be super dodgy, but then you just never go down there. Personally Henriques Street would be a bit too East for me, I wouldn't live further East than Leman street
but I'm a girl and I work late, so *shrug* YMMV.