Good question. It appears to me like a lot “swarm the streets”, either individually or on guided city tours on foot. Others tours the city by the “City train”: Bytoget - Vi viser deg byen!
or the “Hop on Hop off” buses that covers a bit more that just the sentral town area on Aspøy and Nørvøy: Hop On Hop Off Ålesund Sightseeing | Hop On bus tours
Otherwise there are a lot excursions by boat, bus, (or even helicopter) to attractions in the surrounding fjords, or islands.
Here is the recommendations from “Cruise Norway”: https://cruise-norway.no/destinations/alesund/
PS> “3 or 4 thousand pax” is an understatement. Often there are two large cruise ships (<5000 pax) in town together, some days joined by a smaller third ship (>2500 pax)
Last Thursday was one such day, plus the commotion around the wedding this weekend:
