"home to" or "home for"?

Both are widely used and understood. There's even a third alternative, "home of". None of the three is "wrong" in and of itself. However, they mean slightly different things, and in your particular context, "to" is the preposition of choice.

"To be home to X" is a set phrase used precisely for talking about inhabitants of a given place (be it plants, animals, people, or robots). In your sentence in particular, it implies that the diverse flora is already there and has been for quite some time, while home for would imply that the diverse flora is kind of wandering around looking for a home, and now we can offer it one at the Himalayas.

Just to round it up, here are some quick-and-dirty Google stats:

• "home to diverse" — 287,000
• "home for diverse" — 14,000
• "home of diverse" — 47,000

And here are the stats from the Corpus of Contemporary American English (COCA) and the British National Corpus (BNC):

               COCA    BNC

is home to     1451     94
is home for      48      4
is home of       19      1

One piece of advice I would give: "Home for" is often used to designate some kind of charity group house. For example: "Home for Wayward Girls", "Home for battered and abused women", "Home for the mentally disabled", etc. This is probably why the other answers show it being less popular in common usage.

In your case, I don't think I'd chose "home for" unless you want to also give a subtle indication that the place is question is some kind of preserve.