How do I find the index of an item in a vector?

Built-in:

user> (def v ["one" "two" "three" "two"])
#'user/v
user> (.indexOf v "two")
1
user> (.indexOf v "foo")
-1

If you want a lazy seq of the indices for all matches:

user> (map-indexed vector v)
([0 "one"] [1 "two"] [2 "three"] [3 "two"])
user> (filter #(= "two" (second %)) *1)
([1 "two"] [3 "two"])
user> (map first *1)
(1 3)
user> (map first 
           (filter #(= (second %) "two")
                   (map-indexed vector v)))
(1 3)