For your first visit half-day should be enough to get acquainted with the city and its major sights.
Distances are walkable in all cases.
Worthy attractions: University; Capilla San Iglesio; Santos Niños Cathedral.
Left for another visit: Cervantes House; Corral de Comedias; Archbishops’s Palace; Museum of Archaeology.
Last visit: November 2016.

Alcalá de Henares is a pretty university town with many interesting buildings and pleasant streets. The historic center of the city converges on Cervantes Plaza ♥ and stretches along Calle Mayor ♥, which is headlined by the ever popular statue of Don Quixote and Sancho Pansa ♥ sitting on a bench.
Magisterial cathedral ♥ is worth a visit if not truly exceptional.
You can walk through courtyards of the university ♥, but the interior access is allowed only with a guided tour in Spanish. I decided against that. Similar tour is available separately for Capilla San Iglesio ♥ – in this instance, I figured I can take a look even while not being able to understand the commentary, but I was lucky in that I was the only person interested in the tour at the scheduled time and the guide spoke passing English and was nice enough to indulge me.
Many places in town are closed on Monday, which happened to be the day of my visit, so I could not explore Cervantes House/Museum or the historic Corral de Comedias. I also bypassed the Archbishop’s Palace and the regional Archaeology Museum.
If you walk to the edge of town, you can see Puerta de Madrid – a counterpart to Puerta de Alcalá in the capital. They guard roads that lead to each other, hence the names.
Transportation logistics
Trains to Alcalá run frequently from Atocha and take about half an hour one way. The station is within walking distance from the center of town.
Places to Eat
A block away from central square, on Ramón y Cajal, De Juan was a random choice with a possibility to sit on the sidewalk. Nice service, reasonable menu for a comparatively quick sit-down lunch.