Summary - With a three mile, three thousand foot climb, open views of the gorge, and lots of wildflowers, Dog Mountain is a worthy SOTA summit. The first two-thirds of the climb is in the trees, the rest on the windy, exposed mountain crown. The summit itself is thick with brush, so the best operating positions are found on its edge. A Northwest Discover Pass is required for parking, as is a hiking permit during the wildflower season. Check recreation.gov for hiking permit info. This is an incredibly popular hiking destination... plan on going during the week and arriving early if you want to be sure to find a parking space or solitude.
Long version - Dog Mountain, on the north side of the Columbia Gorge, is about an hour from downtown Portland. The easiest drive is on I84 to the Cascades Locks exit, crossing the Columbia over the Bridge of the Gods (toll!), and going east on SR14 to the well-marked Dog Mountain Trail parking lot. You'll get a sense of how popular this trail system is by the size of the lot, which accommodates 200 vehicles. You will need a Northwest Discover Pass to park. April through June on the weekends, you will need an additional permit (recreation.gov) to hike. Pro tip: mid-week is less crowded and an early start (we arrived at 730AM) makes for a quieter hike. If you are up another 1200' or so of climbing, you can hike Wind Mountain (W7W/LC-146) for a double summit day before heading home.
The trailhead is at 200' ASL, making the roughly three mile climb about 2800'. We took the western-most trail up, which is well-maintained and climbs steadily to the tree line at 2400' before crossing the mountain to the summit crown. The trail from this point (Puppy Dog Mountain) to the summit is exposed; be prepared for wind, rain, and in the winter, very icy conditions. The summit itself is covered with dense brush but there is lots of open space in the AZ and some good trees for hanging wires. Set up away from the main path, especially on weekends! You will have views of Mt Hood and Mt Adams, along with the gorge in both directions.
APRS and digital cell service are good, so spotting yourself is easy. The walls of the gorge are between you and Portland and Vancouver so two meter contacts can be challenging. Take a yagi or j pole to improve your odds. HF is definitely the way to go; noise levels are low and even on a day with R2 radio blackouts predicted, I was able to make contacts on forty, thirty, and twenty meters.
With the relatively short drive (from PDX, anyway) nice, moderately strenuous hike and open summit, Dog Mountain is a highly recommended SOTA destination, especially if you avoid the flower-hunting crowds in the spring and early summer.