I know opinions will vary, but I had good water on my trip in late May of 2010, and I recommend part of that, at least the south part. Try to head for McKenna Park, which is a rare, fairly frequently burned ponderosa pine forest. McKenna Park is pretty high quality, and has had low intensity fires in 2003, 2010, 2012, and last year, the ridge leading to it did, too, but White Creek burned hot in the Miller Fire of 2011, so you may choose to avoid that.
Springs abound in McKenna Park, with McKenna Springs being a major one at the south end, and others like Horse Springs in other areas allowing for loops in the park. McKenna was never logged, but it was grazed and had decades of fire exclusion before a fire in 2003 ran through. This initial re-introduction burned an unnaturally thick duff layer and as a consequence, girdled some of the larger pines, allowing for root decay, and eventually wind throw.
If you go, take and post some images, and maybe link them to this thread, too.
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Trails to access and avoid creek crossings are: Leave the area just east of the Cliff Dwelling National Monument on Trail #160, go southwest to trail 162. Hike west on Trail 162 to McKenna Springs, or 187, in the park. The park is McKenna Park, not a park as this is a National Forest, which is a different branch of the Federal Government from the NPS. Stop off the Forest Office in Silver City and pick up a forest map, or at the Cliff Dwelling visitor center if they carry them. The Cliff Dwelling is a National Monument, which IS administered by the NPS, Department of the Interior.
Once in McKenna Park, 187, 155, 153 and 167 can make some nice loops. It has been wet this summer, so there should be water, but you may inquire with the Forest Office, Wilderness Ranger District, if they know or have reports. This area sees few people outside of hunting season, and should be nice, but isolated. If you find you are desperate for water on this loop, go to White Cabin and the West Fork, not White Creek, as flow on White was intermittent on May of 2010, after a wet winter. West Fork requires a lot of creek crossings, if you hike either direction on that, and unless you take stock, I wouldn't do that.
Nothing more enjoyable than a good hike out of town.