Only problem with the Grand Canyon is getting permits. If that is what you want.. apply ASAP.
http://www.nps.gov/grca/planyourvisit/backcountry-permit.htm Also keep in mind that the North rim is closed sometime through May due to snow if one of those hikes tickle your fancy.
March is an interesting time to hike here because March/April there is usually one last winter storm blast in the higher elevations and depending on snowpack, limits access. This pushes you down lower changing things. It is a crap shoot sometimes.
Top of the Mogollon rim is out until April sometimes due to snowpack and closed roads.
Also, a lot of hikes here are short, and the longer ones are just strung together shorter trails, some not very well maintained, so be wary.
This one is along the below Mogollon rim, there will most likely be snow along the trail in march, but it is at ~5500ft so dont know how much unless a late storm hits.
Need to drop a car at one end for this one. Dont even have to do the whole thing, lots of exits, lots of creeks, and springs, lots of trees.
http://hikearizona.com/decoder.php?ZTN=757
Nice loop in the Superstitions.
http://hikearizona.com/decoder.php?ZTN=724
Sheep Bridge
http://hikearizona.com/decoder.php?ZTN=15975
Still looking for more, but there are a few.