I was told that the boat I took from Manaus to Santarem which arrives in Santarem early in the morning would stay in port until the next day. I was invited to leave my things on the boat and return to sleep there rather than going into town for a hotel. I turned down the offer because I wanted to stay a couple days, but if you are just interested in a brief visit you could see everything in a day.
There are two ways of getting to Santarem, by plane or by boat. The fastest and far more comfortable is by plane. Differents air companies have flights to Santarem and most go through Manaus or Belem.
I found the cheapest at Gol although TAM has sometimes good options too, so it's always worth checking out. Buying tickets online is easy.
The airport in Santarem is 14 km west of the city center. Buses run to the city every hour.
Other option to reach Santarem is by boat from Manaus (48 hours) or from Belem (34 hours).
The port (Docas da Para) for the main transport boats to Manaus and Belem is a little ways out of town. It is within walking distance, but if you have heavy luggage or want to save your energy you would do better to take the bus or a taxi. The ticket booths for the boats are just outside the gate to the boat area. According to the vendors their prices are all the same, but as there seems to be some seasonal variation it would seem that you might do well to at least show a willingness to check the several vendors. (One does have to wonder why there are so many agents.)
Boats for lots of other destinations line up along the river in front of Av. Tapajos.