Stockholm is the obvious day trip from Västerås — just over an hour by direct train, which runs frequently throughout the day. The train from Västerås takes you directly into Stockholm Central. Eskilstuna, another industrial city with a good zoo and wildlife park, is 45 minutes in the other direction and worth a half-day.
By car, the area around Lake Mälaren has numerous well-preserved medieval churches and manor houses within an hour's drive. Sala Silver Mine, about 40 kilometres north, offers underground tours through 16th-century silver workings.