By bus (or car) and by boat, there are several interesting side trips you can make within the vicinity of Belém [1]. The most popular destinations are the beaches along the banks of the region’s rivers. Avoid the dirty and crowded ones closest to the city itself as well as weekends, when most beaches are swarmed by day-tripping Belenenses.
Links:
[1] http://www.moon.com/destinations/brazil/the-amazon/para/belem