I might be biased because i happen to live in San Lorenzo de El Escorial (the adjacent town) but I thought I might as well give my POV.

First off the place is HUGE. It's said to be the biggest renacentist complex in the world and It may be the biggest granite structure. It was Built in the 16th century by order of Philip II, during the heyday of the spanish empire and the counter reformation. It houses the Royal mausoleum and a spectacular collection of paintings.

Second, most you cannot visit. The Monastery is divided into quarters only two of which are open to visits, the other two being an active school and a eclesiastical residence. Apart from the monastery, UNESCO also protects several sites you cannot visit, like the underground passages, the fire prevention system, the orchards and the piscifactories. At the time of its completion this was one of the most technologically impressive palaces in Europe. Its monstruous proportions were meant to reflect the power and devoutness of the Habsburg monarchy.

So now...what CAN you visit? Well, the exterior, the basilica, the library, the Royal residences, the mausoleum and a bit of the in between. 

The exterior is sober, not to say almost devoid of decoration. I personally find the style unappealing, though from afar the views are quite good (I recommend going to the herreria to take some photos). The style of the building is called herrerian (after the main architect of the monastery) and it's considered the last an most unique stage of spanish renaissance. The style is characterised by Its grand and sober nature.

The basilica is effectively grand and sober to the point of being cold and even uncomfortable. The altar is worth a close inspection, but overall, It doesn't offer much.

The real highlight of your visit will probably be the Royal residences. The spanish kings were great patrons of the arts and the monastery housed one of their finest collections. Many of the highlights have been moved to the Prado Museum, but the monastery still has a very impressive collection, which is mostly portrayed in the Habsburg residence. The decoration IS not very flashy, following the Habsburg aesthetic, though It's nontheless quite unique for a Royal residence. The hall of battles IS probably the highlight in terms of decoration. A huge gallery showing off the victories of the spanish empire.

The bourbon Palace has been closed for quite some time but It's finally open. Good thing because it's a real treat. The highlight is, without a doubt, the impressive tapestry collection, which covers every square inch of the walls. Many illustruous tapestry makers participated in the making. Goya himself made Many of them when he worked in the Royal tapestry factory. It's overall a Welcome change of aesthetics to the sober Habsburg palace.

If not fascinating these two palaces are at least quite unique, and very different to the standard baroque Palace you find everywhere in Europe.

The mausoleum houses almost all spanish kings since Charles I and an INORDINATE amount of members of the Royal familes. Most of the tombs of the latter group are quite plain, with only a few exceptions like that of John of Austria.The overall atmosphere of the crypt is severe and sombre. The kings and Queens are buried in another hall, even further down, in yet another elegant but plain hall. In comparison to other crypts like the stunning one in Vienna this one comes off as quite underwhelming.

The library (at least the part you can visit) IS small, but pretty impressive. I advice taking a look at the beautifuly decorated muslim manuscripts. The Monastery houses a far bigger, though inaccesible, collection of books, botanical specimes and macabre oddities as Philip V was a great fan of them. 

SUMMARY:

Overall the building perfectly reflects Philip's personality. It's functional (quite cool even in summer) severe and sober. The almost complete lack of decoration and gigantic size definetely give It a very particular aesthetic, which you'd be hard pressed to find in any other palace complex in Europe.

 

IMPORTANT NOTE: IT CLOSES ON MONDAYS.

 

HOW TO GET THERE?

The town IS connected to Madrid through public transport. You can go either by bus (661 and 664 which depart from Moncloa) and trains (from Atocha, Sol, Nuevos Ministerios...). The Monastery is in the dead centre of the old town of San Lorenzo de El Escorial. DISCLAIMER, if you arrive by train, you'll end up in El escorial, which is, confusingly, not the same town as San Lorenzo de El Escorial. You'll find the monastery further Up the mountain. Take advantage of the opportunity and walk through "la casita del principe" a neat Royal park.

OTHER THINGS TO DO:

While you're in San Lorenzo, you can also do some fine hiking. Abantos and las machotas peaks in offers a nice ascent, with good views. The former one also has many botanical oddities.

Nearby you can also visit "el valle de los caídos" the monstruous Monastery Franco built "in remembrance of the fallen in the civil war" (wether they liked It or not...). It's an interesting counterpoint to the monastery as It's built in Neo-herrerian style. It was planned to evoque the grandeur of the monastery, thus the nearby location and similar style. I find the visit quite interesting, it reminds me of the nazi complexes in Nuremberg, though less grand and ruinous.