Uphill from the bus terminal, Residencial El Talquino (Pérez Rosales 114, tel. 065/253331, eltalquino [at] hotmail [dot] com, US$9–11 pp with breakfast) also offers kitchen privileges for a small additional charge.
To the west, 
Casa Perla (Trigal 312, tel. 065/262104, www.casaperla.com [1], US$11 pp with breakfast) offers rooms with shared bath, hot showers, kitchen privileges, and laundry facilities; while it’s not Puerto Montt [2]’s most appealing neighborhood, the sociable owners speak English, and the cozy common areas include a small library.
Nearer the port, responsive Hospedaje Rocco (Pudeto 233, tel./fax 065/272897, www.hospedajerocco.cl [3], US$11 pp with shared bath and breakfast) also offers Internet access and kitchen privileges. Residencial La Nave (Ancud 103, tel. 065/253740, US$11 pp with private bath) is well-located and well-regarded in its range.
Links:
[1] http://www.casaperla.com
[2] http://www.moon.com/destinations/chile/sur-chico/puerto-montt
[3] http://www.hospedajerocco.cl