The
Hotel Mora is up the Paseo del Prado from Atocha...about a ten minute walk....maximum.
It is quiet...even though it is on a busy street, and reasonably priced.
It is not in a high entertainment area.
There are hotels that are closer, like right across the street...and some really nice ones up Atocha (the street) I think there is a new Tryp Hotel.
Hopefully MadridMan and or some of the madrileños will weigh in on this one.
But the Mora will be just fine if you do not find another that you like better.
Good luck!!