Ok, I am going to travel around Europe. I will be in MAD for two nights and I am planning on doing the same thing as the OP. Making the Hilton my base. As I have been plenty of times to MAD, I am not going to visit museums this time, as I will go to Xanadu to ski in the middle of the summer (July trip). The only thing you need is a Metro station to go all the way to the bus station that takes you to the ski slope outside MAD. Also, on my way back from Scandinavia I will be flying out of MAD to the US, so will also go with Hilton MAD Airport.
I am with the OP in the way that you can make Hilton MAD a base for a visit to the city.
By the way, anyone knows if as a HH Gold VIP I will get an upgrade to the executive floor? if not, should I get free breakfast? in this hotel.