Wilson's Snipes have excellent camouflage and are generally silent. Sometimes they feed out in the open, but more often than not these birds are seen after they've flushed. The Gilbert Water Ranch is one of the best places around Phoenix to see these birds and maybe snap a few photos, as the shallow mudflats they favor are mercifully close to pedestrian paths.
They feed the most openly in the mornings and evenings, like many birds, but in my personal experiences I've found them to be more crepuscular, and see them the most often at dusk. Naturally, this makes photographing them tricky.
At least there'll be Dowitchers nearby no matter what when where how or why.