A beautiful day trip from Madrid for a sunny spring day is a trek to La Granja de San Ildefonso. Located in a small town outside Segovia, this palace and its extensive gardens, fountains and grounds are a beautiful spot to explore. If you are really ambitious, this could be a side-trip coupled with a day trip to Segovia, two beautiful places outside of Madrid all in one day.
To get there, you can take either the Sepulveda buses from Moncloa in Madrid to Segovia, or the Renfe train from Chamartin station. From Segovia, you must take the bus (stop is near the aqueduct) and it takes about 15 minutes from Segovia, with those buses running at 45 minute frequency.
The mountains surrounding the town are absolutely beautiful. It is a bit of a hike up and down in parts of the town, so wear comfortable walking shoes. I would also not recommend this trip as a solo day trip, as it is a really nice space to walk and talk with someone, however, it could be a good day alone walking in the gardens if that is what you’re into!
I would recommend to either bring food or plan on eating lunch in Segovia, as the actual town with the palace is very small, and the restaurants are limited in selection and also rather expensive. Bring water, there are public restrooms at the palace however and you do not need to pay for the tour in order to use them.