Is a day trip to Toledo doable/advisable with 3 days in Madrid?

There are tons of things you will miss in Madrid...it's a huge city with plenty of things to do. But, since you are only in Spain for a couple of days, you can do a day tour to Toledo. The AVE takes half an hour each way, but I would try to book as early as you can on www.renfe.es to make sure you get the trips you want, and to avoid standing in what can be long lineups at the ticket windows. Round trip is less than 20 Euro per person.
Unfortunately, many of the sights in Toledo are closed on Mondays....as is the Prado in Madrid. Tuesday would be better, but then you'll miss the Prado, so it depends on what is most important. You will get a sense of Toledo on a Monday, but you'll miss, for example, the magnificent El Greco paintings on display at the museum and the Cathedral.
For tapas, try Plaza Santa Ana....lots of bars and restaurants surrounding, and off of, the square.
And plan to come back!

Thanks for the input, Norm. I was checking out the tour guidebook and it gives hours of operation for Monday in Toledo for both the Cathedral (1000-1830) and Santa Cruz Museum (1000-1800). That's why I was considering Toledo on Monday rather than Madrid, since the Prado is closed.

We were considering a private tour guide from Madrid to Toledo in a car so that we could maybe drive in the countryside with someone who knows more history of the area. Anyone with experience or recommendations? I'm sure we could do it on our own, but just thought it'd be nice to get some insider information about the area.

Thanks again!!

The El Greco Museum, as I've just discovered, is closed for renovations right now.
The Santa Cruz Museum is open on Mondays, so you'll seem some El Grecos there.
I was told my friends in Madrid a few years ago that they closed the cathedral's sacristy on Mondays, which is where all the El Greco painting (and others) were located...that was my chief interest. If they're open on Mondays now, that's great!
The Sephardic Jewish museum and the Visigothic museum are still closed Mondays, I understand....but you should still be able to get an excellent overview of the city and it's culture.
Sorry, no recommendations on private tours...I usually just go it alone.

Norm makes some really good points.

As I see it, all you're going to do in Madrid that is unique to the city is go to the palace and the Prado. (Flamengo is better in Andalucia, tapas are everywhere, so are bullfights -- but Madrid could be best, depending on who's on the program.)

Going to Toledo begs the question of why not Segovia and Avila?

I'd squeeze the most out of Madrid this time around and save the rest for later.

You really have just two full days, right? The Palacio Real can be thoroughly enjoyed in a couple of hours, and you could see the most significant of the Prado’s paintings in a two-four hour visit (personally, I could spend days there). If these are the two must-see sites you really want to experience while in Madrid, then I believe you could do both in one day (Tuesday) and take a long daytrip to Toledo on the other full day (actually Monday). You’re going to miss out on a lot of Madrid, but you’ll have to prioritize what’s important (and you've already got Flamenco and a bullfight covered on your arrival day). I actually had to chop Toledo out of my plan while there in November, but I will return. Segovia has a remarkable Roman aqueduct, but there’s no way you’ll have time for either that town or Avila (Toledo clearly trumps both anyway when you have limited time and are prioritizing). BTW, take the AVE to Toledo and back as Norm suggested. Have fun!