We got this from a blog called Adventure Bimbling. It is not complete guide, nor does it pretend to be, but it highlights some doable stuff that you can do if rain (and typhoon) destroys your itinerary.
I like this part about going indoors such as museum and heritage houses:
Think about everything you wanted to do during that trip. Chances are there are some things that are indoors. Rainy days are perfect for museums, art galleries, wine tastings or even a do-it-yourself tour. One of my favorite things to do on a rainy day is make my own food tour. Find the best places for breakfast, lunch, snacks, dinner and dessert and have fun running around getting to them. You can either enjoy it with a fellow traveler or devour a good book on your own. The day might be a little pricey, but it could very well turn out to be one of your favorite days of your trip.
But also, why not just enjoy the rain?
You can also just ignore the rain. You can simply defy its trip-ruining powers and go about your business. Grab an umbrella, pull up your hood and venture out into the rain. You might find that places are pleasantly empty due to the inclement weather. Perhaps you’ll have certain parts of the city all to yourself. You’ll be soggy, but it’s still a pretty cool feeling to be more or less alone in what is usually a busy place.