I would stay on the east side of the river in the old town. The University is walkable from that area but admittedly up a big hill.
The restaurants as a whole are very good in Coimbra. I usually use Google maps for recommendations. I haven’t been since the pandemic so don’t know which ones might not have survived.
Go Walks has very good walking tours and from their website, it looks as though they have survived the last two years. When I took their tour a few years ago, it included the university library - a must see.
Conimbriga - outside of Coimbra is worth a taxi or Uber. It’s the remains of a Roman settlement with very nice mosaic floors remaining.
If you run out of things to do - Aveiro or even Porto are within an hour or so train ride.