On the Oregon side - you will see 7 waterfalls, including the longest/free falling one in Oregon - Multnomah: http://multnomahfallslodge.com/

Best stops are on the Oregon side, best views are from the Washington side.

I agree with thursdaysd.

To follow that suggestion, pick up WA-14 at Maryhill and drive as far as Cascade Locks. This drive will give you great views of the river and Mt. Hood.

Cross the river on Bridge of the Gods and drive I-84 to Multnomah Falls. From the falls drive on the Historic Columbia River Highway as far as the Crown Point Vista House. Along this route you will encounter several waterfalls. Rejoin I-84 at Corbett for the drive into Portland.

HTtY

Stay on the Oregon side. You get off I-84 at exit 35 onto the Old Columbia River Road past several waterfalls before you get to Multnomah. Are you planning to stay in the Portland area or are you flying out of PDX?
If you have extra time, drive south from Hood River on Rt. 35 to see the east side of Mt. Hood.

There are way more than 7 waterfalls on the Oregon side.

I agree with thursdaysd.

Depending on when you are planning on being here, and if you are planning on driving the old scenic highway on the OR side, be aware that there has been a lot of construction on it this past year and last I heard some of it will still be going on until about April. You can still get around, but may need to backtrack a bit, etc. This is only for the old scenic highway though, NOT for I-84 in OR or hwy 14 in WA.

If you take hwy 14, a few places to stop include the Stonehenge replica in Maryhill, the Maryhill Museum, Maryhill Winery, and Horsethief Butte. The nice thing about the WA side is that there tends to fewer visitors and so traffic is lighter and the interesting stops are not crowded. As HTTY mentions, then you can cut over to the OR side and see the beauty over here.

Be aware that 14 on the Washington side is two-lane and windy in some spots, so a slow go. I-84 is an interstate four-lane highway that's easy to drive.

If you're into wineries, the Maryhill has a nice location but there were several other wineries along the Columbia Gorge.

http://www.winesnw.com/gorgemap.html

We found the Maryhill wines to be only so-so when compared with much better wines to be found, for example, in the Yakima Valley and in Walla Walla. A big pleasant surprise for us late last year was the Bernard Griffin Winery in Richland, Washington. Washington and Oregon are definitely upcoming wine regions to watch and to enjoy.

I second mms's recommendations, especially the replica of Stonehenge. Also on the Washington side, if you're anywhere near the Bridge of the Gods, stop in at the Skamania Lodge. We had a great dinner there of salmon, fresh and cooked the way as only can be found in the Pacific NW.

Multnomah Falls on the Oregon side is definitely not to be missed and should be a highlight of your Columbia Gorge visit.

Um... When are you traveling?