Barcelona was once a Roman city (Barcino, founded around 133 B.C.), surrounded by stone walls. Century after century, trough the Middle Ages this village grow in size and importance. The Barri Gòtic (Gothic Quarter) is a well preserved set of medieval buildings, squares, narrow streets and windy alleys, where you should take your time wandering about (actually, only a few street can be used by cars). You can find roman arches and columns, the cathedral and many churches, beautiful and famous museums along with small boutiques and great places to eat.
At Carrer Paradis, crossing under a Roman arch you can find a set of Roman columns, now inside and part of a more recent building. The scale of the four columns, part of a temple devoted to emperor Augustus, reveals the importance of the original building.
Although it was here where Barcelona history begun, most of the remaining monuments were built between the 14th and 15th century, the time of the Catalonian gothic, and the years of Barcelona as a maritime power.
Almost in the centre of the Barri Gòtic you can find the cathedral, one of the most beautiful Gothic buildings in Barcelona. The Barcelona Cathedral (la Seu) stands at the Pla de la Seu (Cathedral Square) where there is always street animation or small flea markets.
Close to the cathedral, at the Career del Bisbe, you can find the Pont del Bisbe. This portal, toped with a sort of covered bridge connecting the two buildings is what is left from the roman Porta Pretoriae, one of the four doors in the roman wall of Barcelona. The current aspect of the arch is from the XIXth Century.
If you continue down the same street you'll arrive to Plaça Sant Jaume, both the historical and political centre of Barcelona, with the Palau de la Generalitat (the Palace of Catalan autonomy government, that can be visited on Sundays) and, opposite to the Generalitat, the Ajuntament (the Town Hall).
Another must go is the Plaça del Rei (King's Square), a 14th Century medieval public square surrounded by the Palau Reial Major, the Palau del Lloctinent, the 15th-century tower Mirador del Rei Martí, and the Capella Reial de Santa Àgata. On its southern side stands Casa Padellàs that houses the Barcelona City History Museum (MUHBA).
In the west side of the Barri Gòtic you can find the Ramblas, most popular promenade in Barcelona, that extends for more than 1 kilometer, ranging from Plaça Catalunya to the port. At the end of the street there is the monument of Columbus and, thereafter, the Rambla del Mar, an extension of the historic Ramblas to the Maremagnum, a shopping centre in the harbor.
On the opposite side of the district, close to the Via Laietana there is the Palau de la Musica Catalana, the most prestigious concert hall of Barcelona and a true monument to the modernist architecture of the city.
Along the way you will find nice restaurants, bars and coffee shops, lovely antique and craft shops and, in the rambles you cant's surely miss the fruits and vegetables market.