Évora is, undoubtedly, one of my favorite cities in Alentejo. Just less then a couple hours from Lisbon, Évora is a World Heritage Site by UNESCO and its streets and squares hold so much history and charisma that you will find yourself wanting to stay for a few days and to come back as soon as you can.
When you arrive at Évora, the best thing to do is to park your car and stroll around through its narrow streets, finding at each corner something to admire. My suggestion is to start at Praça do Giraldo, (Giraldo's Square) where you can find the Tourism Office (you can get a map there along with useful tips about where to go). This square is the heart of the city, with lots of coffee shops and terraces, lots of shops under the arches of the buildings (you can find traditional cakes and sweets that you must try, if you are a sweet tooth) and the Church of Santo Antão. In front of the church you can find a marble drinking fountain (Chafariz) with eight spouts (representing the eight streets that lead to the square).
On the opposite side of the square, facing the church, you can find on your left the street Romão Ramalho, that leads to Praça 1º de Maio, a large square where you'll find São Francisco Church. Walk inside and visit the Chapel of Bones (Capela dos Ossos), a curious chapel covered with human bones. Close to the square there are the public gardens, where you can walk and rest for a wile in the shade, and the beautiful palace of Dom Manuel.
From there you can go back to Praça do Giraldo, walking by Rua da República. From the square you'll take Rua Cinco de Outubro that will lead you to the front entrance of the Cathedral. Turning left you'll soon find the Vila Flor Square with the Roman Temple (usually called Temple of Diana) and a garden with a great view of the city and the Alentejo plains. In this square you can also find the entrance for the Museum of Évora that, if you have the time, can really be worthwhile to visit.
Going back, return to the Cathedral and visit the interior, the cloister and the rooftop terrace (the view is breathtaking). Évora's Cathedral is the largest medieval church in Portugal and is easily recognized by its unusual conical and asymmetrical towers (rare in Portuguese architecture), its impressive central cupola and by three naves in the interior. Started in 1186 and consecrated in 1204, this fortified gothic granite cathedral was completed only in 1250.
Walking around trough the city streets you'll find many crafts shops with nice pieces to choose. The region is also known for its great wines and you can guarantee to make a good choice if previously you visit the tasting room of Alentejo's Wine (Vinhos do Alentejo) in the centre of Évora. There you get good counsel and you can taste the finest Alentejo Wines before choosing what to buy.