Here's a great hotel suggestion for you, JoAnn:
Villa Real

It is in a perfect location, near the 3 big museums and walkable to the Puerta del Sol. I would stay an extra night if you have the time, then you could see museums on different days, the Royal Palace and get more of a flavor of the city.

I don't think you need a private guide - everything is right there. The hotel can arrange an airport transfer for you, or taking a cab is very easy - as I recall it is about a 1/2 hour drive. Their web site estimates a cab is around 20 euros.

Request a for a room overlooking the front square.