I am looking for an apartment to rent for one person for 3 months in
Rio de Janeiro (starting Now 24 ,2003). I am trying to find  on the
web a few local agencies that rent apartments ie with a local name on
their site. The internation agencies are too expensive for me for such
a long stay. (most charging  a minimum of $60 a day.). Would even settle
for a room in a shared house. Near the beach .

This site might have something you can afford:
http://www.nomorehotels.com/sa/?reg=sa

After going to the URL, type "Rio de Janeiro" in the search box, click
"find," and you'll get lots of possibilities, some expensive, some
not.

G'luck.