I was just in Madrid for a few days and we did a day trip to Toledo. I can definitely recommend it! Getting there by train was fast and easy though we didn’t buy a ticket far enough in advance and had to wait for the next since the train we had been aiming for filled up. Once in Toledo, take a taxi to the cathedral - it’s the best way to get there and taxis are quite cheap in Spain. There’s a charming old town around the cathedral with narrow twisty streets … and a lot of sword shops selling cheap Lord of the Rings -swords. We did find one proper smithy who made real swords as well.
Other than that day trip we also went to a flamenco place one evening. We were the only tourists in the place, so those things are actually popular with locals too. Madrid also has a number of outstanding art museums if those interest you, some nice parks, there’s the royal palace etc. Besides the actual tourist attractions there’s a lot of fancy statues and architecture all around in Madrid when you walk around, reminders of their former glory.
One thing to remember in Spain is that while lunch is eaten as usual, dinner time starts around 9pm so you shouldn’t start looking for a restaurant too early. Our travelling guides recommended ~5% tip which seemed to be enough. Especially at lunch “the menu of the day” was usually very good and cheap, something like 12e for 3-course meal and a glass of wine.
That was a bit rambling post, hope you’ll find at least parts of it useful. Enjoy your trip, we certainly enjoyed ours. 
Going to Spain this summer. My daughter gave me the Lonely Planet book on Spain. In reading about Madrid, it says that the music (I like jazz) starts at 1 am. And people party until sunrise.
I have been booking rooms on Airbnb. Cheaper and you get to mingle with the locals. Plus a lot of them let you use the washer. Very convenient for me, as I will be traveling very light.
Yes, and you can either take a bus with a guided tour or just ride the commuter train. There’s two sinagogues, the Greco museum, way too many tourist shops, enough restaurants and bars to eat each meal in a different one for a month without leaving the Old Town and that area is tiny. Plus, just the Imperial Gate is damn spectacular.
I didn’t visit the Military Museum (which got moved from Madrid to Toledo’s Alcázar a few years ago) because I’d already seen it in Madrid.
Another day trip from Madrid that’s absolutely spectacular is Segovia - the Alcázar there is the most beautiful of Spain’s Christian-built castles. Try the roasts.
No need to tip, as service is included. Tips above “keep the small change” should only be given for super-spectacular, “I’m going to tell everybody how good this place was” service.
A great day trip from Barcelona is Sitges, which has a ton of Modernist houses (take the train). I think by the time you’re here, Barcelona will have a new Moderniste house available for visiting; well, the house is actually one of Gaudí’s earliest jobs, but until now it was a private residence and couldn’t be visited. Two other cool day trips are Montserrat and Figueres; for foreign visitors I’d recommend Figueres (including the Dalí museum) over Montserrat.
The number of people wearing jeans in Europe has shot WAY up since the first couple times I was there.
Hell, if you don’t want to stand out in Italy, just wear those weird red jeans you see every now and then. They seemed to be a thing in winter 2010 in Italy, and in Belgium and the Netherlands in 2012.
I really think it’s the shorts, tennis shoes and t-shirts that give away most white American tourists as Americans; all tourists have camera bags and other travel accoutrements.
I know, it was just amusing to be told to not dress like an American but to (paraphrased) “just wear a style of pants invented there.” 
Well, in the summer pretty well everyone is a tourist so I wouldn’t worry, though not looking completely clueless might help. There’s a lot of mobility in Europe now and there are people - mostly from the poorer eastern countries - who will take advantage.
One way to help blend into the crowds: buy an Aldi or Lidl shopping bag to hold what you’re carrying. Many Europeans use them to get their groceries home even if they didn’t buy the food at Aldi or Lidl. They cost 10 cents each, are fairly large, and surprisingly sturdy for the price. Because they often contain bottles, jars, and cans, it’s not unusual for them to get big and lumpy. I’ve used them to carry my dSLR and extra lenses, bottle of water, newspaper, no problem. Something to consider.