Andrews Bay in Seward Park is a great place to do some open water swimming. It is relativly sheltered from the wind and chop, and it is a no wake zone for boats which means that they'll generally be going quite a bit slower.
There are some rules about where you are allowed to swim, and these can be seen on the Seattle Parks and Recreations Depts website (or do a google search for "open water swim seattle"), but I've never heard of swimmers getting hassled by the police in this area.
There is a large amount of triatholon swimmers who like to practice here, and the distances between landmarks are pretty well known. The standard place to enter the water is just north of the Pottery building, a good 50 feet from the swimming beach at a little jetty.