Being the 5th oldest country in the world we had many different presences and influences brought trough our navigators... your culture can be seen an "adapted" mix of that all.
Portugal has a lot of roman and arabian architecture left, most converted into museums, exibhition excavation touristc sites and some still in use, or are part of renovated buildings. Aqueducts and churchs sites are the major elements of roman architecture but you can also find great exemples of housing (villas), roads, terms and city walls. More relevent then the ruins is the know-how they left us...
can explain you some of the roman presence in Lisbon and on the region around the city.
Conimbriga is the largest and most extensively excavated Roman site in Portugal. It's near Coimbra, the city you refered but Coimbra is known for having the oldest college in Europe still working and not for it's roman architecture.
Mostly at the South of the country you can find arabesque influences, a few like in Carthage (in mordern Tunisia). carthaginians lived here (not yet Portugal bu Lusitania) around 200BC but soon left, being expulsed by the romans.
ps. Hannibal did founded at least 1 town here. It's called Alvor and it's situated in the Algarve... http://www.portugaltravelguide.com/en/portimao.htm