Round Mountain is a road hike of about 2 miles one-way and 1000 feet of gain. It's close to Lookout Mountain-W7O/CE-039 so you might consider doing both of those peaks.Note that there are FIVE Round Mountains in Oregon, with one in CE near Lakeview. This is the Round Mountain east of Prineville.

Head about 16 miles east of Prineville on Highway 26 to Ochoco Creek Road, a slight right turn. Go 8.3 miles to Ochoco Ranger Station (camping possible), and then bear right onto Canyon Creek Road for 6.8 miles where you'll note the turnoff for Lookout (signed for Independence Mine and Round Mountain Trailhead). Yes, you can take a trail from here to Round Mountain - it's twice as far and has more gain, but some might prefer a trail vs. a road experience or not have a high clearance vehicle. This description is for the shortest hike. 

Continue 2.2 miles to turn left onto Round Mountain Road. It's been paved roads until here. You'll take Round Mountain Road for 4.2 miles. My GPS wanted me to turn onto NF-220, but don't be tempted - keep on the main track. The road is mostly well graded gravel degrading to dirt after a while, but some places would challenge a passenger vehicle.

You'll arrive at a gate with room to park. From here there are eight or nine switch backs, depending on how you count, and about 2 miles of road walking. 

The summit has a small RF site - no interference was experienced from it. There are no handy trees at the site, so rigging a HF antenna right on top isn't easy. I was able to balance my backpack to support my pole and sit in the shade of the RF equipment. There were flies. 

HF propagation was very poor on my afternoon up there and I relied on three random 2m FM contacts, and one non-chaser on 20m CW. Locals suggest that you try 146.52, .50 and .58. This is apparently the site for the N7CCO repeater, 145.210 MHz (-0.6 MHz), tone 141.3 so calling there could help.