Taking Devon to the North Branch trail and hence to the Green Bay trail will serve you better. Foster is unduly south, and the lake further east than you need to be, plus by entering the lake at Foster you miss most of the good parts.
If you want to do the Great Chicago Bike Trail tour, take the Blue line, transfer to the Green line, and go down to the Garfield stop, ride your bike east, get on the lake, ride north until you run out of lake, follow the north bike signs to Loyola university, then go west on Devon, stopping for Indian food at one of the dozens of excellent options (I'm partial to Tiffin, me), and thence to the North Branch trail, which runs through the Forest Preserve and is very beautiful. Better start your day early for that one. Most of the beauty of the lake can be seen by going Blue to Red, Red to Roosevelt, and then east a few blocks to the Museum campus, route following the lake as before but skipping ten or so miles down south.
Get the map, it'll help make this stuff clear. Enjoy your stay!