The main area is around the [remote] visitor center if you’ve never been. It’s very close to where the perennial forks of the Gila River meet and has a neat exhibit in the visitor center, plus a huge weather radar display. There’s extending the Woodland Loop that can usually take 3 days if going counter-clockwise … there’s a lot of stream crossings on the Gila’s Middle Fork, but Jordan Hot Springs (which are “warm”). There’s also taking a day to visit the cliff dwellings especially if they let visitors step into said dwellings themselves. Then car-camp at one of the free camp/trailhead units.
To extend the Woodland Loop, there’s a number of trails to the south of the visitor center that all connect to each other. We would go up from TJ Corral TH and climbing up and over a ridge, settle in to an early campsite with water going down the far side. Next morning hike along the ridge’s trail until Electric Canyon Trail, then go down to the West Fork. There’s some stream crossings and campsites along the West Fork, plus a couple trails going into the Woodland Park area mesa. If it’s rainy there even may be some flowing creeks on the mesa but if not you may need to pack some water (though there may be standing water on the mesa). Anyways to get to the Middle Fork, there’s a number of trails along said Mesa to get you there. Most decide to go into the Middle Fork to camp on its banks.
In the morning you can decide to go down the middle fork with stream crossing (wet but guaranteed water) or stay up on the mesa. Either way you can reach Little Bear Canyon Trail that takes you to Scorpion campground and a mile back to the visitor center.
Getting there: Silver City is the gateway town from Tucson, Albuquerque or El Paso. They’ve been trying to become the major trail town of the nearby CDT fwiw including its trail days in mid-May, so check if there’s any last minute outfitters (most were bicycle oriented last I time I visited a few years back, but the CDT keeps getting more popular).
It’s a drive but taking the flat road through San Lorenzo takes you past a restaurant for little loss of drive time vs the winding road from Silver City. (Probably not enough time for a modified detour via the CDT I guess if taking AMTRAK).
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