We will be staying at the W Lakeshore in Chicago. Is it safe to swim in Lake Michigan. If it is safe, how far from the hotel or Navy Pier to get to the swimming area.

It is safe to swim in Lake Michigan and the city has around 30 miles of beaches. The closest, and within walking distance of your hotel, is tthe Ohio St. Beach just north and west of Navy Pier at Olive Park.

http://www.chicagoparkdistrict.com/resources/beaches

Although the park district list indicates that distance swimming is available at all the beaches it actually isn't possible at many of them. And at many the life guard don't allow people to go out where it is deep enough for swimming. It is, however possible at Ohio St--all the way to Oak St. Beach. I don't like to swim there though because the water always feels a bit oily, due probably to the fact that many yachts anchor a short offshore just about every day.

My favorite place isn't on the list. It's the redundantly name Promontory Point in Hyde Park, It juts out about 1/4 mile into the lake. The water is deep enough to really swim and the view from the north side of the Point is one of the best in the city--not to bad from the other side either. See:

http://www.hydepark.org/parks/point/prompointpark.htm

Today, June 1, the water temperature was 60F. And it will be getting warmer See:

http://weather.noaa.gov/pub/data/raw/sx/sxus83.klot.omr.lot.txt

Yes it's safe to swim, but only in designated areas.
The closest beach from W Lakeshore or Navy Pier would be the Oak St beach, which is less than a mile north along Lake Shore Dr.
Or you can walk further north to the North Ave beach, which is less than 2 miles from the hotel.