We stayed for 2 nights at the end of our trip. I was looking for a room or rooms to sleep 3 adults (parents and college-age son). I also looked at hotels that had 'suite' type rooms that might fit a rollaway bed, which we have done in the past.
I had a bad experience with a noisy room in Barcelona years ago so i did a ton of research. Many on this forum have recommended Hotel Europa, but i was hesitant due to its location on the busy square of Puerta Del Sol.
I also considered Hotel Catalonia las Cortes, but it turned out to be booked for my dates.
I ended up with two adjoining rooms at Hotel Preciados, which were separated from the hallway by an additional door, so we could leave our room doors open while we were in our rooms, which was nice and i'm so glad we spent for two rooms. They were 150 euros each. This included a minifridge with free drinks inside (there was also room left if you wanted to put your own stuff inside).
I did not know that the Hotel would be undergoing room renovations during our two-night say, but it was only taking place from 9-5, so did not bother us. if you are booking in the next few months, you might want to ask about this.
Hotel Preciados is on a pedestrian street which limited the noise. Our rooms were at the end of the hall on the 2nd floor. I didn't find out until the 2nd night that in addition to blackout curtains there were motorized metal rolldown shutters, which really made things quiet.
Hotel Preciados did not have a free breakfast but they had a VERY extensive buffet for 17 euros, so that was nice for our last two nights.
We also ate in the restaurant after arriving by train in the evening, because we wanted to eat early. So it was nice to have that option - the food was fine, the hotel restaurant has good reviews online, but it's certainly more for tourists/travelers than locals.
I liked the neighborhood we were in as it was extremely central. we had also considered staying by the museum/retiro area, but for 2 nights i really liked the walkability. Madrid is very large and can be overwhelming on a short stay (especially since we had gotten used to Sevillle!)
hope this helps!