It is not essential, as long as it is walking distance/quick tube hop (like one or 2 stops max) does not have to be a stones throw away, especially for the right place. A bit of luxury would be nice, but not essential, as us just being away together without a toddler is luxury enough!
I stayed in the Caesar a couple of years ago. At the time I got an upgraded room with fruit, bathrobes and water etc for about £70 a night including brekkie, was very nice and trendy. It's in a quiet street but is close to Hyde Park and the Bayswater tube station. There's also a lot of cheap eateries around there. I think it was booked thru lastminute but you could try www.travelsupermarket.com and compare hotel prices.
There is a lot of schneiders around that area so watch out. We stayed at one, I think it was called the New London.....looked fab on the website but it was a bombsite when we arrived.