For your visit one day should be sufficient.
Distances are mostly walkable, although the aqueduct is located outside of town.
Worthy attractions: St Mary Cathedral; Murallas (Roman Walls); Roman Circus; Ponte del Diablo.
Left for another visit: Roman Amphitheater (looked on outside only).
Last visit: August 2016.
Tarragona is a pleasant and attractive town, with a compact historic center that is not too overrun by tourists. There are many inviting squares and streets to stroll, but the main attractions in town all relate to its Roman history, comprising the UNESCO World Heritage site.
Things to See
Roman walls ♥ offer a good walk and plenty of historic information on the stands along the path. You will be able to see how the walls grew in different eras.
Roman circus ♥♥ is well worth the price of entry. It consists of a number of underground spaces as well as open-air ruins, with information on how the place and the Roman city around it functioned. Torre de les Monges, located on the site but often listed as a separate attraction in guidebooks, is nothing too special.
There is also an Amphitheater, which we only looked at from the park above. Its location is close to so called Balcony of the Mediterraneo ♥, a promenade high above the sea.
Tarragona Cathedral ♥♥ is airy and light, not too ornamental but boasting brilliant mosaics. The cloister is among the highlights.
A few minutes outside of city center, Ponte del Diablo ♥♥♥ is a well-preserved Roman aqueduct that can be walked across. It anchors a park with several miles of trails, for those inclined to hiking.
Poblet Monastery ♥ is a UNESCO World Heritage site with some interesting features both on the interior and the exterior, but on balance not extraordinary enough to warrant a visit for anyone not devoted to exploring places of worship.
The tours run about once an hour and are conducted in either Catalan or Castellan; visitors not speaking either get a booklet with brief explanations and explore on their own without following the guide. The tour starts with cloisters and adjacent rooms, continues into the church, then onto the upper floor, and through a number of other spaces. Following a guide may provide better appreciation for the place.