Some places are changing, either naturally or economically. I would go to these places first.
Natural change means a place used to be virgin, quite undeveloped and natural, but while more and more people are visiting, it will become different in the future. That's the reason why I went to Andaman Islands.
I have to brag here. When I was rafting in the Amazon jungle in Ecuador, our trip was the first ever commercial trip in that specific river section. Sounds cool? :)
Economic change typically comes together with natural change. When I went to Andaman Islands, the accommodation cost was triple to 3 years ago. (My Lonely Planet guide was 3 years old.) I prefer to go to places while they are still cheap and nice.
Some other touristy places are quite mature and stable. These are typically cities and parks in developed countries. For these places, I'm not in a rush. I'm pretty sure that they stay the same over years or even decades. :)