Hmmm. so many options. I'll give you three of my favorite.
1. Middle fork of the Gila River, we call the 'Meadows loop' Meadows loop is 3-4 days, but You can add some extra miles continuing up the conyon and make the trip as long as you want. This is a AWSOME canyon hike, with lots of easy river crossing and tall canyon walls(hundreds of feet high) and HOT SPRINGS. Very scenic. Water will be no problem along this route. It's fairly easy hike with only a few climbs.
2. Reeds Peak, via Mimbres River. It's about a 5 day trip. Two full days to make it to reeds peak and a day to explore around the peak and ridges, and two days back home. This is one of the least traveled areas in the Gila National forest and one of my favorites. You start at lower elevation in mimbres canyon and acsend up to 10,000 plus feet in to sub alpine forests. You will have water all along the Mimbres river (More like a creek) and there are multiple springs at and around reeds Peak.
3.Cat walk redstone park loop. This is a 5 to 6 day lolly pop loop. You stay mainly in White water Canyon for the hike expcept for a climb out of white water and into the south fork of white water, for the route back. Very nace canyon country. Water is not a problem.
There are many more good trips into the higer country. like the Mogollon crest trail, and Black Range Crest trail. But these hikes you have to plan your trip according to were the springs are. There are lots of springs, so it'sot a big deal. But it will be colder up there and probably some snow in certain spots.