You can use expose.sh to expose your server using a public HTTPS URL.
Install expose.sh
For Mac or Linux, go to Expose.sh and copy/paste the installation code shown into a terminal.
For Windows go to Expose.sh, download the binary and put it somewhere in your PATH.
Expose your api to the web
Start your API server. Then run expose <port>
where port is the port your API server is running on, like 80 or 8080.
Expose.sh will generate a random public expose.sh URL. You'll see output like
https://s3rh.expose.sh is forwarding to localhost:80
http://s3rh.expose.sh is forwarding to localhost:80
Then you can get Stripe to use the public HTTPS URL, which will forward to localhost.
I've written a full guide here
Disclaimer: I built expose.sh