As usual in these big cities, I really suggest Priceline’s “Name Your Own Price.”  Last time we got a wonderful and modern hotel in the Camden Town area for a low price.  Start at 70 dollars for the lowest and work your way up to 100.  You only get to try with one credit card every 24 hours.  Have at least 2 handy.  Choose areas that are more in the middle of town and not the outskirts.  London is a huge city.

Suggestions for nice areas:

Camden Town (maybe not for grandparents though)
Covent Garden
Notting Hill
Hampstead Heath (a little farther north but very cute)

You don’t want to stay in the Docklands.  It’s very modern and fine, but WAY out of the way.