The Alentejo around Évora is rich in megalithic sites and small towns worth visiting. The Cromeleque dos Almendres and the Menhir dos Almendres are only 15km west and easily done as a morning excursion. The Anta Grande do Zambujeiro, a massive dolmen about 13km southwest, is one of the largest megalithic chambers in Europe — the capstone fell in the 20th century but the remaining uprights are impressive.
The towns of Estremoz (about 46km northeast) and Monsaraz (50km east, on the Spanish border) are both worth a day trip. Estremoz has a hilltop castle and a market famous for local cheeses and the regional figurines known as bonecas de Estremoz. Monsaraz is a medieval hilltop village barely larger than a football pitch, overlooking the Guadiana river and the Alqueva reservoir; the views are extraordinary.