On the same side of the river (and very close to the Southbank Centre), the County Hall Premier Travel Inn offers rooms at �99 per night, for up to 2 adults and 2 children:
http://www.premiertravelinn.com/pti/hotelInfor mation.do?hotelId=23881&iscsell=true
Check availability here:
http://www.premiertravelinn.com/pti/makeBookin g.do?tiibsId=LONCOU
Just beyond the Premier Travel Inn, you come to the Marriott County Hall:
http://www.marriott.com/hotels/travel/lonch-lo ndon-marriott-hotel-county-hall/
It's delightful but double room prices range from about �350 per night to �650 per night!
(For both of those hotels, the nearest Underground station is Waterloo but, except when carrying luggage, it's often simpler to travel to Westminster and walk over Westminster Bridge).
On the opposite side of the river to the Southbank Centre (i.e. just a short walk over Waterloo bridge), there are several pricey hotels, including the Savoy, the Waldorf and the Swissotel Howard. Rather cheaper (at �149 for 2 people in a twin or double room, with breakfast) is the Strand Palace Hotel (which has received favourable comments from Answerbank contributors):
http://www.strandpalacehotel.co.uk/
(The nearest tube station, for the Strand Palace, is Temple. Charing Cross isn't much further away).
Returning to the south of the river, you might also want to consider staying at the Mad Hatter:
17:29 Thu 30th Aug 2007