I am sure there will be some festivities, but you really should be in Reykjavik on June 17th. A lot of folks come to Reykjavik from the countryside to partake in the city parades and festivities, with EVERYONE being out in the streets in Old Town with all types of entertainment and a number of band stands throughout. Family time during the day, but the party goes on all night.

Ódinnthor is right, the main festivities are in Reykjavík, which will be very crowded on our National Holiday with a lot of fun activities. There are festivities in Stykkishólmur on this day as well with the parade starting at 13:00 and different activities which last through the day. And a family ball starting at ca 20:00.