Alenquer (2 days) – Across the Amazon River from Santarém, the village of Alenquer was founded in the 18th century by missionaries attempting to convert the local Alvaré Indians. Alenquer has several impressive waterfalls relatively nearby, including the Cachoeira Aço das Pedras. The town is also the gateway to Ciudade dos Deuses (City of the Gods), a field of bizarre rock formations 50 km north of town. Another 50 km farther is the Vale do Paraiso (Valley of Paradise) which has a fine pousada and additional waterfalls. (source: Lonely Planet travel guide)
Monte Alegre (2 days) – The sandstone hills behind Monte Alegre, about 120 km downstream from Santarém, are dotted with caves and bizarre rock outcroppings. They in turn are adorned with dozens of rock paintings believed to be around 11,000 years old, the oldest known human creations in Amazonia and possibly Brazil. Most are in red and yellow, and depict human and animal figures, plus geometric designs and hand-prints of the painters themselves. (source: Lonely Planet travel guide)
Parque Nacional da Amazonia (3-5 days) – Created in 1974, the national park is located on the banks of the Tapajós River and occupies an area of 994,000 hectares. The best time to visit is the dry season, which is July to October. The park has diverse forest types within its boundaries and up to 40 different flora species per hectare. The tallest trees reach more than 190 feet high. The park also has a tremendous diversity of animal species, including river dolphins, the harpy eagle, the giant anteater, the Amazon tortoise, and many others. A full description of the flora and fauna can be found here.