+1 - AWS Systems Manager Session Manager [1] is the future! (although it does have a ridiculous name...)
It's free, and configuring its agent can enable you to do other useful maintenance tasks through it.
Assuming you're using Amazon Linux 2 as your AMI, it's just as simple as assigning a instance profile with the right permissions (you can use the managed AmazonSSMManagedInstanceCore policy [2]).
And you'll then be able to connect through the AWS Console or CLI.