This most difficult aspect of this route description will be the drive up FR278 on the west side of Mt. Antero. From the intersection of FR277 & FR278, (Upper Baldwin Gulch TH) head SSE on 278 continuing up through forest until you reach the last trees at just above 12,000 ft. The road turns east and heads briefly up a gully before making the first of six sharp switchbacks to gain elevation on the flank of Antero. After the sixth switchback, the road heads generally south and crosses a ridge at 13,100 ft. This switchback section of the road is the roughest and most tedious part of the drive (or hike). If hiking this section, attempts to shortcut the switchbacks will lead to frustrating loose rock conditions on a very steep mountainside.
At the ridge crossing at 13,100 ft., there is a fork in the road. Going left grants access to Antero and Mount White. Stay right for Cronin and the route to Cyclone & Carbonate, and also UN 13,712. The ruggedness of the road relents and cuts downhill to the SW through tundra to an intersection at 12,670 feet where you can pull off and begin a hike for Cronin, if you've managed to drive this far. Another option is to lose another 200 feet in elevation and park at a switchback at these coordinates: N 38° 39' 01.02" W 106° 16' 15.04". , still for Cronin, Carbonate and Cyclone. Elevation is 12,460 ft.
If your goal is UN 13,712, continue down past this switchback into the Browns Creek upper basin area. The road heads generally ESE for a while, then turns south, followed by a broad turn back to nearly north before going directly east. If driving, park in the vicinity of these coordinates: N 38° 38' 43.95" W 106° 15' 29.04". Begin the hike from here. You should be just a short distance north of Browns Creek. You may be able to find a good campsite in this area.
From the road, the first order of business will be to find a way across the creek and through the willows with a minimum of effort. IN 1995, we found a shaky log across the stream about 50 yards down from where we started. (Likely not there any longer.) On the other side of the creek, a wade through some tall willows may be required for 20 yards or so. Try to emerge on a minor ridge that will be clear of timer for a while. Drop Se into a small basin with a small, unnamed lake that shows on the USGS map right at the 11,400 ft. contour. In 1995, we fould a game trail that led us around the west, then south side of the lake. Next, head SE through timber, gaining elevation and making possibly a couple of minor creek crossings before gaining a couloir at about 11,600 ft. that comes down from just SW of the summit of UN 13,712. You may walk for a while in the gully, but it's easier to cross on out to the east side and gain the NW ridge of UN 13,712.
It will be rocky crossing the gully and getting onto the NW ridge, but once on the ridge you'll enjoy a pleasant tundra stroll for quite a ways up. There's even a faint old mining road bed that will lead up the ridge to the last tundra at about 12,900 ft. From there, continue on medium-sized rubble/talus, though in some places there will be talus that approaches boulder size, similar to the final ascent on Mt. of the Holy Cross. At 13,200 ft., gain the more north-south running ridge and head directly to the summit on easier & better footing.
A short story about climbing etiquette: The day we climbed this summit, it was going to be Tim's last summit in completing the Top 200 ranked in Colorado. Now you would think that accompanied by his family, they would have afforded him the honor of tagging the summit cairn first. However, Shaun, our 12-year old son, feeling his Wheaties that day decided to race ahead of Tim as they approached the summit and in a show of male dominance beat him to the actual summit, but then condescendingly withheld tagging the summit cairn until Tim arrived a minute later and would do so. (Actually, we were kind of pleased that at this point in Shaun's life, he was finding his own motivation to climb these peaks.)
Since Jones Peak bears a name, even though it is not a ranked, 13er summit, some may be motivated to go ahead and bag it. It lies on a long, rocky ridge east of UN 13,712. It took us about 45 minutes each way to traverse that ridge. The first third of the traverse requires working your way over, around and down various rock formations that are slow and a little tiresome but not overly difficult. The next middle third section of the ridge goes quickly on mostly tundra & embedded rock, and the final third requires a climb back up to the ridge crest on loose talus and more scrambling over large boulders. There are a number of apparent high points. We tagged them all until it was apparent the ridge was losing elevation. On the return, we stayed more on the ridge crest avoiding where we had descended too much on the south side on the initial traverse.
For those interested in bagging Tabeguache and Shavano from UN 13,712, here's some description: The hike to the saddle between the two 14ers from UN 13,712 is easy on mostly tundra. Once at the saddle, follow the ridge east and south to the Shavano summit. It's a long haul weaving in and out among boulders. Return back to the Shavano-Tabeguache saddle. Ascend the east ridge/side of Tabeguache on medium talus & rubble with any number of trails leading through.
Links to other information, routes & trip reports for this peak that may be helpful.