Jones Mountain's East Ridge is approachable either on its own or in conjunction with "American Peak". The "American Peak"-Jones Mountain is a fine two summit traverse so I will focus on the route as it pertains to combining the two summits.
Drive to the Cuba Gulch Trailhead from Lake City; or as far as your vehicle can make it.
To get within striking distance of Jones Mountain follow the Snare Gulch Road from the Cuba Gulch Trailhead. After Ascending the Snare Stairs (better to walk them in my opinion but then I dislike 4 wheel driving). From the above timberline Jones Mountain is the unimpressive hump at the head of the drainage and "American Peak" is the ridgeline to the right. From here the actual climb begins.
From where the 4 wheel drive road emerges from timberline the routes are obvious. The ascent of "American Peak" requires leaving the road to cross rolling tundra to the east. Aim for the more solid looking portions of "American Peaks" south ridge (testy scree abounds around here). Once on the ridgline proper the route becomes obvious and "American Peak's" summit is easily gained. From the summit of "American Peak" there is aspectacular view of Jones Mounntain.
To continue the traverse follow "American Peak's" southwest ridge contouring around the couliors and minor summits. This travers has a use trail and is quite enjoyable. As one approaches the "American Peak"-Jones Mountain saddle the views of Jones Mountain become much more impressive. This saddle is where the "American Peak" traverse meets the Jones Mountain East Ridge.
If doing Jones Mountain alone merely follow the 4 wheeldrive road up to where it makes a sharp turn crossing a creek and then leave the road, proceeding up towards the "American Peak"-Jones Mountain saddle. The terrain around here varies from rolling tundra to San Juan style talus. At the saddle join the "American Peak"-Jones Mountain traverse.
From the "American Peak"-Jones Mountain saddle ascend the very well defined ridge. This section looks tough from a distance but is not bad at all. It exempifies the joys of the San Juans. After several little summits and notches the summit is attained. Joy! Enjoy the spectacular scenery, lounge about, and then descend. Jones Mountain's summit view is even better then Handies Peak's (I think that is saying alot).
Just working legs and an appetite for alpine beauty. Winter would be different. If you are willing to ascend Snare Gulch in the winter the actual climb should prove easy. Surviving the Snare Gulch approach would be the hard part.
If you have information about this route that doesn't pertain to any of the other sections, please add it here.