Both of them were in my budget...3 nights. Wanted a luxury hotel, central location (near piccadilly and jubillee line). Good service.
Ohh and i have a 2 year old with me...so just a nice place incase the weather doesn't turn out to be very cooperating...to be able to sit inside and/or just walk close by for a quick easy bite.
Idea isn't to see all sites, but rather 2-3 sites and do them slowly and enjoy them properly.