Not far from Tower Hill, and East of The Shard, lies the Wapping waterfront. An interesting area with a bit of history and character attached: and increasingly expensive like a lot of London. Having said that, when you are priced out of central London, expense is relative.
A lot quieter than Soho, it will take a bit of getting used to but it has its advantages. After the hustle and bustle of the West End, a quieter environment might even be one of them. Home on the bike via London Bridge and Elephant and Castle is a bit of a rat race though. Cycle routes to and from Wapping is a work in progress! A lot of regeneration has been going on down by the river for quite a while.