Östra Ågatan (lit. “The Eastern River Street”) runs down the east bank of Fyrisån. There is nothing on Östra Ågatan that you're going to need in your first few days.
Although you won't need to go there in your first few days, Gotlands nation is on Östra Ågatan.
The river runs almost exactly southeast in the very centre of Uppsala, and the streets are oriented accordingly, it otherwise runs through town about south-southeast, but people generally think of the river, and the streets parallel to it, as running north-south, so having an “East Bank” and a “West Bank” makes some sense.
Smedsgränd, Bredgränd, and Bangårdsgatan all run perpendicular to, and end on, Östra Ågatan. Gamla Torget lies on this street, and (of course) crossing the river over Nybron or Dombron leads, not surprisingly, to Västra Ågatan.