Take a walk through the grounds of the Washington Park Arboretum, along the edge of Lake Washington, and near the grounds of the old MOHAI building. This is a nice urban romp, perfect for before or after work, or on a day when you just can't get out of the city.
From the trailhead on E Foster Island Road, walk parallelling a marshy body of water called Duck Bay--an appropriately named small inlet off of Union Bay in Lake Washington. As you walk, look for kayakers or the eponymous ducks paddling about.
The trail here is wide and dry, with plenty of room for people and bikes to pass. Walk across a pleasant open forest and cross under Hwy 520, emerging onto a little hillock, where you can access a beach on the large lake, with views of UW stadium.
Hang a left onto the Arboretum Waterfront Trail, stopping to take a peek at a map which has the trail's length and a general map of the area laid out for your perusal. Continue down the path, which now skirts the wetlands of Union Bay through a tunnel of vegetation well over six feet tall onto Foster Island. Turnpike and boardwalk are here to keep hikers' feet dry, but the boggy nature of this area means that despite the structures, the trail can be quite muddy, even impassable in high water.
If you can get through this section, you'll cross the water on boardwalk and soon arrive on Marsh Island, with views across to the UW campus and boats cruising Union Bay. Lilypads edge the trail here, and you may even see great blue heron fishing nearby.
Soon you'll pop out onto dry land near the old site of the Museum of History and Industry (MOHAI). The trail takes on an urban flair here, as you skirt the south edge of the MOHAI and cross over Hwy 520 on 24th Ave E.
Once over 520, turn left onto Lake Washington Boulevard and follow it around to East Miller St. Directly across from East Miller St a rough path heads into the grasses beneath two freeway access ramps. Take this path, and follow it around and under the access ramps to the edge of another marshy body of water, where you'll find ducks swimming and diving for food. You're nearly to the end of your walk at this point. Continue just a few hundred more yards until you pop out onto the pavement of E Foster Island Road, just short of where your car is parked outside the Arboretum.