In spite of the fact that the city has six million inhabitants, traffic congestion as bad as in any major European city, and 2 main summer months that are as hot as you know what, Madrid is a remarkably easy and (yes!) relaxing city to visit and get around in.
For a start, there are no messy customs requirements like visas to arrange before you go; and once you've arrived and settled in, there are plenty of well-informed tourist offices in both the city and its surrounding province to give you the lowdown on what to do and where to go. Transport by metro (subway) and bus is extremely efficient and frequent, with an increasing number of facilities for travelers with disabilities.
The currency is the euro (€), common now throughout practically the entire European continent -- with a few stubborn exceptions, like Norway -- and it's easy to combine visits to other countries, such as England and France, without having to worry about changing currency. (The only downside at the time of writing for American travelers is the poor exchange rate of US$1.60 per euro.)