If it wasn't Winter, I would recommend going east from Portland up the Gorge (The Dalles, Hood River, etc); great scenery. And sometimes you can find an accidentally nice day in January or February.
Another option is the coast (about a 90 minute drive), again depends heavily on the weather (unless you like Winter storms). Cannon Beach and south are where to be. But Astoria is nice; great maritime museum, lots of Victorian bed and breakfasts, and quick jaunt across the river to Washington (Long Beach, Seaview, Oysterville).
If you like snow and mountains and icy roads, then go east (and slightly south) up highway 26 to Mount Hood and Govt Camp. Very, very, nice.
Going directly north or south from Portland doesn't offer much in terms of tourism or scenery.
I suppose this post is probably too late.