If You Have 1 Day--Start your day in Washington Park at the Rose Garden (the roses are in bloom from June to September) and the Japanese Garden (lovely any time of year). After touring these two gardens, head downhill into downtown Portland. If you can make it to Pioneer Courthouse Square by noon, you can catch the day's weather prediction on the Weather Machine sculpture. From here, head over to the South Parks Blocks and visit the Portland Art Museum, which usually has some big show going on. Across the park from this museum is the Oregon History Center, where you can finish your day. If it's the weekend, be sure to squeeze in time to visit the Saturday Market (open both Sat-Sun; closed Jan-Feb), in the Skidmore Historic District.
If You Have 2 Days--Follow the outline above for your first day in town. On your second day, head up the Columbia Gorge to see its many beautiful waterfalls. If you get an early start, you can loop all the way around Mount Hood and maybe get in a little hiking from historic Timberline Lodge.
If You Have 3 Days--Follow the 2-day strategy as outlined above. On your third day, explore some of the historic blocks in the Old Town neighborhood (take in the Saturday Market if you haven't already), and perhaps visit the Oregon Maritime Center and Museum. Then walk through Tom McCall Waterfront Park, at the south end of which you can catch a historic trolley that runs to the posh suburb of Lake Oswego. Alternatively, you could take a scenic cruise on the river or do some paddling on a guided sea kayak tour on the Willamette.
If You Have 4 Days or More--Follow the 3-day strategy as outlined above. On Day 4, head over to the beach; it's only about 1 1/2 hours away. You can stroll around artsy Cannon Beach and explore nearby Ecola State Park. Then make your way down the coast, stopping at other small state parks along the way. You can head back to Portland from Tillamook. If you have time, do part or all of the Three Capes Scenic Loop outside of Tillamook before returning to Portland.
On Day 5, venture north to Mount St. Helens for the day to see the devastation that was caused when this volcano erupted back in 1980. Along the way, you could stop and visit historic Fort Vancouver in Vancouver, Washington. If you're a wine fancier, skip Mount St. Helens and instead head west from Portland for some wine tasting.