Coimbra is a university town with a number of attractive features, coming out no more than ok on balance. The university – a UNESCO World Heritage sight – is well worth the exploration.
The historic core of the university – Alta ♥♥ – is located in the highest section of town, occupying the former Royal Palace and a number of surrounding buildings. “Program 1” itinerary obtained from the ticket office will take you to the key places. The palace ♥ has a couple of impressive spaces and terraces. São Miguel Chapel ♥♥♥ is beautifully tiled, painted, and decorated, with a very colorful organ. The tower ♥ climb is not for those who are claustrophobic or overweight, and the views from the top are at best so-so (although you get a good look at the fountain on the river), but it is still a pleasant diversion. Note that there is a tiny extra cost to climb the tower via a separate ticket. Finally, Biblioteca Joanina ♥♥♥ is amazing. You get less than twenty minutes to enjoy it (and no photography is allowed), but it is definitely a marvel; you also get to look into the academic prison and the library archives, which are not as impressive, but still add to the overall picture.
Access to the library is on the timed-entry basis. There is no way to reserve time in advance, and on busy days it may be sold out fairly early in the day. On the positive flip side, if you are lucky with your timing, it can take less than 2 hours to see all of the university core.
The vast central plaza of the university, Pátio das Escolas ♥ is quite impressive as well. Outside of it, imposing buildings – quite a few of mid-20th-century pedigree – and various statuary comprise the larger university grounds.
Science Museum is also the part of the “Program 1” ticket, but it did not fit into our itinerary – it is some distance away from the university core.
There are several other points of interest in the upper town. New Cathedral ♥ blinds with its opulent altars. Old Cathedral ♥ has a number of fetching features, such as tiled framing of its chapels and an understated cloister with plenty of small details. Botanic Garden ♥ is a pleasant park, but also short on knockout features (possibly it is more impressive in the period of bloom).
Church of Santa Cruz ♥♥, at the foot of the upper town, is probably the most impressive of all non-university sights – its organ is spectacular, and its azulejo-covered walls are exquisite. The church is free to enter; for extra fee, you can explore the entire monastery that it is part of, which we decided against.
A couple of other potential attractions fell out of our itinerary. Coimbra is considered a hotbed of Fado music; the daily performances at Fado ao Centro start at 6pm, which was later than we could stay in town. We also did not go to reputedly interesting historic park Penedo da Saudade, which was a few minutes extra walk away from the central area.
The lower-town part of the university, Sofia, named after the street around which it is clustered is not especially impressive – you would not necessarily even distinguish university buildings from the rest of the area. UNESCO site inscription also mentions Santa Clara Monastery on the other side of the river, but that also could not fit into our schedule.