A college town, León [1] caters easily to those looking to stay on longer. Room for Rent posters are found easily around the universities and on bulletin boards of the main hostels. In general, expect to pay $150–200 a month for a room with shared kitchen and up to $400 a month for furnished apartments.
Check with Jordan Clark (tel. 505/8672-3566, www.nicaraguarealestateleon.com [2]) or Green Pathways Tours (www.greenpathways.com [3]); both keep lists of long-term rentals in León and shared houses on the beach.
Links:
[1] http://www.moon.com/destinations/nicaragua/northwest-coast/leon
[2] http://www.nicaraguarealestateleon.com
[3] http://www.greenpathways.com