If you look hard enough you can find a job without a TESOL Certificate. However, I wouldn't minimize the importance of having one. And if you do decide to get a certificate, I would suggest avoiding the online programs. Many of them are scams and not worth a plug nickel. There are some good schools in the States that are intensive one month programs and would be well worth the effort and the cost.
As for teaching in Asia without a certificate, it varies. I can only speak first hand of my experience and extensive searching for good jobs in China, but I think it's generally the same all over Asia. You can find a job without a certificate, especially with your qualifications, but the best jobs are those that require one. Albeit, a word of advice; be very careful when choosing a job. If possible, avoid agents. English teaching has become such a lucrative business that corruption is rampant.Communicate directly with the employers at the school, and talk to someone who is working there as an EFL teacher or has worked there in the past. In other words, be very careful. Right now, schools in China, Korea, and Taiwan have the worst reputations for honoring their commitments. But that's not to say it's impossible to find a good job with kind and honorable employers. Just do your research.
Now, even though you mention that money is not an issue because of your financial condition, please don't accept a job for under 7000RMB if you choose to work in China. Others will disagree with me on this point, but the truth is that they can all afford to pay much more than what is generally offered and accepted. Personally, I won't accept less than 7000 and that must include all the ammenities; free, unshared housing (Western style), all utilities paid, water dispenser provided and water paid, computer provided (with internet access paid). Also, make sure you will not be expected to work for more than 25 hours max, and that there is a provision in your contract for a raise if your students respond to your teaching after a given time agreed upon by you and your employer. Having said all that though, please be aware that a contract will generally not protect you in China. It's for them not you. Don't accept a contract that stipulates a payment to them if you break the contract. Agree on a one month trial period. Never sign a contract until your passport is in your hand with the work visa already provided.
Finally, remember that Chinese are practiced and shrewd negotiators. They love to say yes when they mean no. And no can often mean they're only testing you.
Good luck.