Stating near Aldgate East station?

Define character.

Cobblestones and hidden alley ways?

Cultural diversities?

Dichotomy of architecture?

What exactly are you seeking during you stay in London?

In over 25 years of London visits have watched this area evolve.

I guess I meant street-level activity like little shops or pubs, people walking around, street entertainment, and so on.

You're on the fringes of The City of London, so there's a lot of high rise office buildings.

Whitechapel is a racially and culturally diverse area. Lots of people that would identify as "asian" in British parlance, which would generally mean people from south Asia; the Indian subcontinent and surrounds. You're spoiled for choice for eating Indian food in Whitechapel, Bethnal Green and Brick Lane. There's a vibrant street market every day (except Sundays) on Whitechapel Road. It is focussed mainly on the asian community, but it's something to see. I'm not that familiar with pubs in this area, but I'd bet my bottom dollar that it's not hard to find some proper ungentrified east end boozers if that appeals.

The Whitechapel Gallery is a bit of gem, focussing on the contemporary side of art.

Brick Lane is a short walk and there's lots to see there in terms of quirky shopping and street food. Beigel Bake is a big favourite for filled beigels (bagels) and is busy 24-7. I made a point of going to E Pellici on Bethnal Green Road for a mid-morning full breakfast recently, and it's a worthy contender for best cafe in the whole of London.

As you go up into The City, you have the all the hustle and bustle of an international financial district in the daytime, but it can be a bit quiet at night. There's lots to see here too, from the ancient remnants of London Wall, to Norman Foster's [edit: Richard Rogers actually, like the Pompidou in Paris] Lloyds Building, arguably the finest modern building in London (certainly my favourite). Spitalfields is another great area, with a hip market daily and one of my favourite churches, Hawksmoor's Christ Church Spitalfields

The nightlife of Shoreditch is a short walk.

Lots of this area was totally wiped out in WWII, so there is a real mix of the old and new. Many places have also been demolished and redeveloped several times in the post-war period. What I like is when you see a glimmer of the ancient among the modern. This area really rewards the curious. As is the case with many areas of London, scratch the surface a little and there's threads of history going back centuries. It's somewhere you'd get a lot from a guided walking tour.

GerryM has throughly and thoughtfully described the neighborhood.

If you are looking for a proper pub experience try both the Princess of Prussia and The Brown Bear.