From Madrid · 40.42° N · 3.70° W
Four getaways with a night away and three day trips from Madrid for 1 May and Dos de Mayo, chosen for what spring brings: full lagoons, beech woods in new leaf, vultures nesting and the Strawberry Train.
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In May the Rodeno pine woods no longer have snow, the days are long enough for the paintings and an afternoon on horseback, and the heat of Teruel has not yet set in. Albarracín fills up at midday on long weekends: sleep inside the old town and do the cathedral and the castle with a guide first thing.

In spring the lagoons carry more water and the falls linking them run strongly, which is when the waterfall route looks its best. The summer heat has not yet reached the paths and the park is not yet full of swimmers: book the kayak and the Cueva de Montesinos.
In May the Montejo Beech Wood puts on new leaves and the passes are less in demand than in autumn; the online draw opens on the 1st and 16th of each month. The Beech Wood is closed on Mondays, so go on the first day, and in Patones the rock is dry and mild for the introductory climbing session.
At the start of May the climb to the Laguna Grande may still have snow in the high areas: ask in Hoyos del Espino the night before. If there is, swap the route for the south face of the Puerto del Pico, lower and in full spring, with the Cuevas del Águila and Arenas.

The Strawberry Train runs its spring season, which includes the May long weekend, from the Delicias Railway Museum to Aranjuez in wooden carriages. You arrive in time for the guided palace tour, the Isla gardens in bloom and the boat on the Tagus.

At weekends and on public holidays the Canto Cochino barrier stops cars in mid-morning, when the quota is full, so this plan starts before 10:30. In spring the La Pedriza streams run full and the granite does not yet burn.

In May the griffon vultures in the canyon have chicks in the nests, and from the canoe you can watch them going in and out of the walls. It is nesting season, with restricted areas from January to July: the Casa del Parque, in Sepúlveda, tells you which before you go up to San Frutos.
Questions
Yes, it is the holiday of the Community of Madrid and applies across the region. When it falls on a Sunday it is not always moved to the Monday: check that year's working calendar.
There may be some on the peaks of Gredos and Guadarrama, especially on the climb to the Laguna Grande. Ask at the visitor centre before you go and have a plan below the snow line.
Yes, its spring season includes it. It leaves from the Madrid Railway Museum and the tickets for the long weekend sell out early.
The nearby ones, Aranjuez and the Sierra Norte, an hour or less away. For the distant ones, leave very early on the first day or the afternoon before.
Geocaliahttps://www.geocalia.com/en/spain/community-of-madrid/madrid/getaways/may-long-weekend