Formerly an industrial zone, Shadwell is a diverse, working class neighborhood in East London. This is an affordable part of the city, but not a particularly desirable one. That means you'll get more space for your money, but there's not much going on culture or entertainment-wise.
However, Shadwell is well connected to the rest of the city by transport: you have access to a few train stops and several bus routes.
The City: 2.1 miles / 15-25 minutes by car / 10-15 minutes by transit / 15-20 minutes by bike
Canary Wharf: 2.1 miles / 10-15 minutes by car / 15 minutes by transit / 30 minutes by foot / 10 minutes by bike
Southwark: 2.4 miles / 15-25 minutes by car / 20-25 minutes by transit / 15 minutes by bike
Westminster: 4.4 miles / 20-50 minutes by car / 30-35 minutes by transit / 30 minutes by bike
Shoreditch: 2.8 miles / 15-25 minutes by car / 25 minutes by transit / 15-20 minutes by bike