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When people first come to Portugal usually go straight foward to Lisbon... I know it`s a well known city, but you have so many good place to go. And very near the airport, about 15km you can go to Almada.
Is where I leave... and I love it.
You have amazing parks to ride a bike or do a picnic, and you can visit the Cristo-Rei. It`s a monument very big, very similiar to Corcovado in Brazil.
You can come by ferry boat... it`s very pleasant and you can do some sight seeing.
Maybe the best thing here for turism is the beaches... you have Costa da Caparica. The best ambiance to take a nice bath and play voleyball with your friends. Next to the beach you have many bars, and at night it can be very entertainment.
And if you like art, you have many places to visit contemporary art or go to see a theather.
Also, the restaurants serve many fish dishes, so it`s very healthy and tasty! =)
If you`re interested you can see this info here: http://www.m-almada.pt/xportal/xmain?xpid=cmav2&xpgid=genericMenuContent&menu_title_generic_qry=BOUI=17109535&menu_generic_qry=BOUI=17109535&genericContentPage_qry=BOUI=3831474&actualmenu=17109535
*pictures not mine, see souce link*