Pittock Mansion, because it is situated on a steep hill high above the city. My group took this advise and took the twisty road that led to this mountaintop beauty. It is not a road a giant RV or 18-wheeler could navigate, but most passenger cars will fit the road just fine. We stopped on one of the main streets leading to the mansion access road to pick up carry-out meals from Subway, so we could have a picnic on the grounds, since it was a beautiful SUNNY window of opportunity in this frequently-overcast city. The views were magnificent, and it was clear enough to get a glimpse of The Cascades in the distance. Plus, the city of Portland was spread out before us, allowing us to find our hotel, the river, and other landmarks. This outing could be an entry for "Budget Travel Tips" because there is free parking, free bathrooms, free water fountain, free strolling of the grounds, free picnic table/benches, and free scenic views. If one is determined to spend money, however, there is the ever-present gift shop with lots of pretty trinkets, as well as an inside tour of the home that is available for a fee.
So if you find yourself in Portland, get out of your pit at the Pittock! (If you are not in Portland, but still feeling "in the pits", read Beth Moore's book "Get out of that Pit!")