Not sure what you mean by "The Hood". I suspect that you really mean Hood River which is at the other end of the Gorge.

You could drive I-84 to Hood River and cross over the Bridge and take Hwy 14 back on the Washington side. According to www.weatherunderground.com there is a 90% chance of rain at Government Camp so you are probably right that it makes little sense to go up to Timberline. You can stop on the way at Multnomah Falls and enjoy the rain.

Another day trip would be to take Hwy 26 west to the coast and south to Cannon Beach. Routing would be 217-26-101. Stop at Cannon Beach and look around, proceed south as far as Tillamook or alternatively Lincoln City and return via Hwy 6 from Tillamook back to Hwy 26 or Hwy 18 to Hwy 99 to 217 from just north of Lincoln City.

It is an easy 1.5 hours to Cannon Beach, another hour or so south and about 1.5 hours back to Portland. If you like to drive, this is a nice drive.