Aussieflyer and I spoke privately .. but this was my reply ( for the benefit of other board members in a similar situation ) :
Puerta del Sol is the absolute centre of Madrid . Ground zero for the whole of Spain , and it's from where , officially , all distances are measured in thw whole of Spain ! When I first came to Madrid I stayed a total of about 8 weeks living here . In Puerta del Sol itself there are mainly only hostales ( very basic 1 or 2 star style hotels ) .
Having worked as a trader in London's financial markets I got to stay in some very glitzy hotels , but I made a decision to stay in hostales this time . They weren't bad ! But some are very old and don't have elevators .
The 4 and 5 star hotels will be in streets off of Puerta del Sol ( All VERY central ) . Puerta del Sol is noisy and full of life , but also they have some building work going on there at the moment ( A new metro line ) .
Gran Via is Madrid's main street ... full of shops and eating places... Not my favourite street , but very dear in the hearts of the Madrid natives .
Plaza Mayor is the main square and very central .
One other area is Chueca ... equivalent to London's Soho . It is the centre of Madrid's gay community and has a very quirky and lively nightlife .
Finally , there is Plaza Santa Ana , with it's beautiful hotel ( Reina Victoria ) .
All these places are within a 1 mile ( or less ) square of the absolute centre of Madrid .
Take a look at www.hthoteles.com they have a few very central locations and look very smart ... No idea of the cost though .
There are some very good hotels also , such as The Ritz , but remember that European cities are expensive .

Don't hesitate to contact me again if you need other information .