I just spent a quick two days in Madrid on my way home from the UK. Here's some travel impressions:
-I can't believe that I took so long to get to Madrid. I've now been to 30 countries and just now got to the 3rd largest city in Europe (behind London & Paris.) It was definitely a mistake on my part. Madrid is waaaaay more interesting (and fun) than some of the 2nd tier cities that I've been to.
It did seem, though, that Madrid is a tiny bit off the beaten path. There are - for example - many more flights between the US and Paris or even Frankfurt than Madrid.
Also, Madrid lacks a signature event or icon. I had a great time in Madrid and really enjoyed the sights and the history, but there isn't a single prominent must-do/must-see, like the Eiffel Tower, Big Ben, or the Duomo.
Most memorable in Madrid's case is the food & drink, or perhaps lifestyle. Not only are tapas tasty, but it is an insight into Spaniards way of life.
2 things surprised me about Spanish food: 1) it wasn't spicy at all, and 2) it tended to be very basic. For example, 2 of the most common tapas are patatas bravas and albondigas, which are roasted potatoes with ketchup (more or less) and meatballs in tomato sauce. (Not a complaint - I enjoyed them both.)
So to experience Madrid, come hungry. (And be sure to visit the Mercado de San Miguel, which provided the single best hour of touring that I've ever experienced. It's a market/food court that offers the best of Spanish food in a very accessible way/)
It's true what they say about Europeans taking the whole month of August off - the town was fairly quiet and there was wide availability at restaurants and hotels. It's also true about the proclivity for siestas in the afternoon.
As for trip specifics, I stayed at the Hotel Tryp Diana, a 4* hotel near the airport. The hotel was decent, and a 7 minute walk to the Alameda Olmos Metro stop on the end of line 5. (Line 5 running through the heart of the tourist districts.) The hotel area is nearly 100% residential, though there are a few restaurants/pubs focused on the locals, including 2 located inside the hotel.
I wish I could have spent more time in Madrid, and I'll definitely put a higher priority on exploring the rest of Spain.