You also may want to consider the Philippines. It may be a little more expensive to reach, but the internal flights are generally pretty inexpensive and there's certainly enough to do here to kill a week and a half. You don't need a visa, people speak English, and Filipinos are very friendly and open and like to engage with foreigners, especially Americans. You can basically avoid foreigners if you want to by staying out of the more expensive resorts. The tourist infrastructure isn't as established as Thailand, but it's easy enough to get around for a first timer.
Putting that aside, i haven't been to Phuket, but I did enjoy Chiang Mai for the most part. The first time I went, it struck me as a backpackers' haven, which isn't far from reality. It's a jumping off point to neighboring countries like Laos and likely now Burma. I stayed largely in the city and didn't love it. I appreciated it much more on my second trip because I hired a driver for three days and got outside the city to some of the surrounding villages. I don't know about prices these days, but in the past 10 years, the PHP has appreciated 10% while the THB has appreciated close to 50% compared to the US dollar. I was surprised when I was last in Bangkok how expensive things had become, in part due to inflation and in part due to exchange rate differences. I wouldn't personally bother going to Pattaya unless you are completely out of things to do in Bangkok, which isn't going to happen in a few days.