The hints are pretty sparse because Severian doesn’t know where he is any more than the reader does, but Wolfe confirmed it in an interview here: https://www.depauw.edu/sfs/interviews/wolfe46interview.htm

But yeah the river is a big hint. The Paraná in Argentina is a good candidate, and it’s easy to rule out other big delta rivers like the Nile or Mississippi. Iirc Severian also uses the word “pampas” for plains, and at some point we learn there’s a jungle zone to the north, with an arid region beyond.