Nassau for 3 month

Hi!
I am Daniel form Graz, Austria (Europe). Me and my girlfriend are planning
a trip to NYC in November. After NYC we'd like to visit Nassau for 3
month. I would like to
do a little work there, maybe in an architectural office (I am an
architect). We do not think about a "Hotel on the beach holiday" but we
are seeking for the feeling
of "living in Nassau". So I wonder wether it is somehow possible to find
an affordable flat to rent for that time, or to find some work to do for
me, uncomplicatedly.
Coming from Austria, we do not know the bahamas very well. Has anyone done
something like that?

regards, Daniel