Dic's list matchs my list as a good starting point for walking about. Add the Market Square which is a block from the Senate Square and a fun place to roam when the vendors are out. Market Square has anything from Russians selling fur caps to food stalls.
Look over Rick's list and pick what looks good to you. Most can be linked into a walking route with the Folk Museum and the Suomenlinna Fortress being obvious exceptions not being in City Center. The Fortress, accessable by ferry departing near the Market Square is a good several hour visit.
▲▲▲ Temppeliaukio Church Awe-inspiring, copper-topped 1969 "Church in
▲▲ Uspenski Orthodox Cathedral Orthodoxy's most prodigious display
outside of Eastern Europe.
▲▲ Lutheran Cathedral Green-domed, 19th-century Neoclassical
▲▲ Seurasaari Open-Air Folk Museum Island museum with 100 historic
buildings from Finland's farthest corners.
▲▲ Suomenlinna Fortress Helsinki's harbor island, sprinkled with
picnic spots, museums, and military history.
▲ Senate Square Consummate Neoclassical square, with Lutheran
▲ Helsinki City Museum Tells the city's history well and in English.
▲ Ateneum, The National Gallery of Finland Largest collection of art
in Finland, including local favorites plus works by Cézanne, Chagall,
Gauguin, and Van Gogh.
▲ National Museum of Finland The scoop on Finland, featuring folk
costumes, an armory, czars, and thrones; the prehistory exhibit is
▲ Sibelius Monument Stainless-steel sculptural tribute to Finland's
▲ Design Museum Chronological look at Finland's impressive design
pedigree, plus cutting-edge temporary exhibits.