I set up a web site 13 or 14 years ago, and I'm trying to figure out where

Based on the information you've provided, it's unlikely that the website you set up in 2011 or 2012 is still running on a free tier or free service from AWS. Here's why:

1. AWS Free Tier: The AWS Free Tier is typically available to new AWS customers for 12 months following their sign-up date. Given that you set up the site over a decade ago, any free tier benefits would have expired long ago.

2. Static Website Hosting: If you hosted a static website, it's possible you used Amazon S3 (Simple Storage Service) to host the files. However, S3 is not a free service, although it is very cost-effective for small, low-traffic sites.

3. EC2 Instance: If the site required any server-side processing, you might have used an EC2 (Elastic Compute Cloud) instance. Again, this is not a free service beyond the initial 12-month free tier period.

To locate the website, you could try the following steps:

1. Log in to the AWS Management Console using the account credentials you used back then.

2. Check your billing information or cost explorer to see if there are any active services incurring charges.

3. Look through the various AWS services, particularly S3 and EC2, to see if you can find any resources related to the website.

4. Check your email for any AWS notifications or billing statements from over the years.

If you're unable to locate the website through these methods, it's possible that the site is no longer active or has been removed due to inactivity or non-payment. In this case, you may need to set up the website again if the client still needs access to it.

Remember, AWS services generally aren't free beyond the initial trial period, so if the site has been running all this time, there would likely be some associated costs.
Sources
Just activated my account, but free 12 month free-tier is expired | AWS re:Post
Microsoft FAQ – AWS