Can I say "peerless mission?"

Solution 1:

You certainly can. An article in The Washington Post titled "For Searchers in Iraq, a Peerless Mission" did just that. It may not be the most common phrasing, but it is valid.

As per the comments, unique shouldn't be equated with peerless. Someone may have a unique hairstyle, but that does not make it peerless (the best you've ever seen, surpassed by none). Likewise, an actor may give a peerless performance (an unmatched rendition of Hamlet), but it may not be unique (others have done it, just not as well).

I agree with FumbleFingers that the construction sounds awkward and isn't one you'd find on a typical basis.

Solution 2:

Here is a peerless mission ... near Santa Barbara, California...