Washington Park and the Zoo are close into town. You can take the MAX train to the zoo. some of the trees in Hoyt Arboretum should also be in bloom. MAX is the lightrail train that runs east and west from Downtowm Portland. If you are downtowm, the Pearl district has some great restaurants (too many to mention here). NW 23rd Avenue is a great walking street with trendy shops, restaurants. The trolley will take you to NW 23rd. On Saturdays, head down to Saturday Market for some great finds. Walk along the waterfront at McCall's waterfront park. Cross over one of the bridges to walk along the East Bank Esplanade for a great view of the city.
If you have extra time and a car, you must drive up to the Columbia River gorge (up I84 about 40 minutes). In April, the leaves should be out and the waterfalls will be at their full force. Multnomah Falls, Wahkeena and Latourelle are really nice. It would make for a beautiful day. Have lunch at Multnomah Falls for a real treat.
This is from my wife, who has lived in the Tigard/Portland area for about 25 years:
Hi there, as a lifelong Oregonian, even if I don't still live there, I have lots of great ideas. If you are staying downtown, be sure and take advantage of the MAX for across the river, and main route transportation. The downtown Marriott location, on old Front Street, now MLK, gives a nice view, but is too far from the heart of the city. Closer locales to Broadway, Burnside, and access across the river are more "Rip City" originals. Try to take in a Blazers game at the Rose City, take the Max. If you want a great view, go to the Portland Rose Garden, where the real award winning roses are grown in the summer. Even when the roses aren't out yet, the view is amazing, and the names of all the local queens of Rosaria, the mythical kindgom, are on display. Go up old Burnside to the Rose Garden, and if possible take in the Pittock Mansion, an original home of an old city banker. View of all the mountains can be seen there on a clear day, Hood, Adams, St . Helens and Rainier. The Portland Waterfront Park hosts the Fun Center during the Rose Festival when the US Navy fleet comes in. There are 3 parades, and I took my kids to all 3, the Junior, Starlight and Grand Floral. Go early, sit on the sidewalk, and bring chalk to draw pictures on the sidewalk.
Jakes and Ringside are always mentioned as great restaurants, but other secrets exist. Try Dan and Louis Oyster Bar, down near the Benson Bubblers. The Spaghetti Factory is right on the Willamette River. For breakfast, try the Original Pancake House off Barbur in the southwest for a giant "baby" pancake. One of the newer spots to try is VooDoo Donuts. Roses Deli in the Northwest has a great Jewish deli. Portland has lots of great food, and coffee shops are all over. Go to the Washington Park Zoo, home of the greatest bunch of elephants around, including the much loved *****. Go in April, and the city has a big birthday party for him, and we all eat carrot cake. There is a Ducks Store downtown, outlet for the University of Oregon Football team. Go sit in Pioneer Courthouse Square, Portland's living room, have a coffee, and just watch the folks go by. Get out and drive a little, go to Estacada and see the Clackamas River, and keep going to Mt. Hood. The other way, on Highway 26, routes to the Oregon Coast on the Sunset Highway.