Definitely echo the advice to try and step outside Zone 1 if you can find something. Hammersmith is quite well connected and in Zone 2, good connections - the Piccadilly line will get you into central London nicely, District line will get you down to the Thames, you can even snag the Central line reasonably easily if you head up a few stops and change, can't remember the exact station name atm.
If you're trying to stay close...ish to Waterloo - Pimlico can be that wee bit quieter.
Hotels wise there are quite a few smaller ones, Lady_Lenny and I stay around Paddington when we're in London - plenty of smaller cheaper hotels but they can be a bit hit and miss, couldn't really recommend any off the top of my head sorry as we tend to stay in the Hilton Hyde Park now. Happy to dig through my records though, but most of my direct experience is in West London, so may not be super helpful if you wanted to try and stay closer to Waterloo itself
Lady_Lenny's parents rented a small apartment near Portobello road a few years back that was excellent - but you'd probably have more options via Airbnb these days.