Solomon Butte on a map looks like it has roads going everywhere but it really doesn't. To get to a good start you will want to get to RD 4504 that somewhat circles the summit part way up. This is a jeep road with some tight pin striping opportunity in some areas and soft pumice your tires will sink in in other portions. We camped at 42.70679, -121.80856 with the idea we would go up a well used road FS4502-400 up the south corner but this road was being used as the exit road for logging trucks early morning and just too dangerous to go against them. We never saw a truck but we heard the jake breaks all morning and could see heavy tracks. So we went around the east side until we reach the north side of the mountain to find a good starting point up a old logging road, at least part way 42.73733, -121.79870. It was around 1.5 mi round trip, stay to the east within the older timber as you climb up and you will be good, otherwise you will get tangled up in a lot of manzanita brush.
The summit is a combo of solid manzanita, a cool rock formation, and some tall timber. I found a little clearing to set up in after bushwacking about 20 yards in thick brush. May be some better opportunity.
As I approached the summit I saw the rocks and to me it looked like a head resting on a pillow so I called it Solomon Sleeping ;)
de AG7GP