If staying at the Strand a reasonable place to eat (i.e. new mortgage not needed) is Rosso's in the circular building the other side of Hakaniemen, it also has nice views across Toolonlahti (
http://www.rosso.fi/menu-in-english/) Rosso is the down market restaurant of the S-Group (a Finnish Coop group). There is also a Rosso in the Walkway between Stockmans and the Central Railway Station.
Many of the down town restaurants are very expensive and mainly designed to be seen in. One cafe I would recommend is Karl Frazer Cafe Kluuvikatu 3 between Alexandersgatan and North Esplandai. Close by is Strindberg cafe which is a Helsinki institution.