Steve Cole and I mounted 4834' Monument on Saturday, 22 November 2003, in a brisk one hour and thirty-two minutes. You can find detailed planning info in Patty Furbush's "On Foot in Joshua Tree" and Andy Zdon's "Desert Summits". Monument Mountain is the highest point in the Hexie Mountains.
Monument Mountain is accessed most easily via the Cottonwood entrance of Joshua Tree, and the five miles of good but slow dirt on Pinkham Canyon road. It's a straightforward trail-less saunter of the south ridge, traveling approximately three horizontal yet gently rising miles of the long ridge before hitting the steep-ish summit cone. Furbush calls it 1500+ elevation gain, but my Avocet told me closer to 1800. We successfully dismantled many unnecessary and objectionable cairns along the way. If you can't figure out which way to go on a semi-narrow ridge.....
We were blown about by strong gusts of wind on the ascent, at times losing balance. The windchill was rather arctic, calling for my balaclava! on the whole stroll. Monument's summit register was placed in 1994, yet the pocket-sized notebook was only half-full. Since Monument is not on any lists, the list-types don't get up there (but they should). Mark Adrian had an entry from 1995, I think. The register was also hands-down the most entertaining register I've ever perused, and others within it also agreed. It also seems - according to our experience and to previous entries - that Monument is typically quite windy, so go prepared. Surprisingly, I counted many more ascents from out-of-staters and out-of-country'ers than I did from CA residents. I surmise that it may have something to do with Monument's proximity to the visitor center, the commanding view, the lack of 'listing', and the ease with which one may summit. Many entries were from east coast visitors, in addition to Germany, Ireland, and England. I would approximate that Monument only sees about one dozen parties per year. There was one entry about one week before us, and then none preceeding until March 2003.
For the view and ease alone, Monument should be on your 'list'.
If you've got a 4WD, I would also suggest that you complete the additional fifteen miles of the Pinkham Canyon descent to I10. You can find details in Tony Huegel's "California Desert Byways", but beware that he calls it easy to moderate. For the most part, the whole thing is, but the 2003 monsoon season really tore up the second half of the twenty-mile journey. There is one definite high-clearance and 4WD mandatory section, where I earned my first (very minor) body damage on my 2002 Toyota Tacoma while negotiating the second tricky crux (the two cruxes are about fifty feet apart).