levitation allows you to levitate over mines, can't walk over mines with belt of carrying and ring of searching. ring of searching doesn;t always detect all traps - I have stepped on them before while wearing ring of searching. Belt of levitation also allows you to fly over water (go to attnam without killing/teleporting/silvaing Genetrix versana, go back to new attnam to kill decos without going through UT again), fly over acid (frog blood or slime vomit can destroy your boots, you don't get stuck in slime), belt of levitation allows you to set traps and lure baddies over them without worrying about springing them yourself.
As for what to wear instead of ring of searching, I like a ring of invis, or electricity resist, or polycontrol, or telecontrol (if i haven't got permacontrol from blink dogs) or acid resist if fight acidic enemies (frogs, slimes)