The Strand Palace Hotel is just along the road from the Aldwych Theatre (and Waterloo Station is just over Waterloo Bridge). For a random date I selected in December, the cheapest price offered on their website is �129 for two people (including breakfast):
http://www.strandpalacehotel.co.uk/
However, the price is only �121.03 if you book via the Ryanair website:
http://www.ryanair.com/globals/partnerurls/red irect.php?language=EN&culture=GB&partner=EXPHO TELS&pos=NAVTAB
(With only one exception, everyone who's submitted reviews to the Ryanair site has given it high marks).
There are more luxurious hotels in the area, such as the Waldorf Hilton (which neighbours the Aldwych Theatre) and the Savoy (which is opposite the Strand Palace) but they're not cheap. (Prices at the Waldorf start from �183. I daren't look at what the Savoy charges!).
Chris