How long do you have to wait to reapply for a Thai visa after rejection?

First figure out the reason why it is rejected. Then you may apply again immediately.

If I've been rejected once, would it be better to apply to another city in the same country? Or would it be better to apply to a different country altogether?

Can apply the very next second after denial.

I waited 1minute before opening a new application. The embassy told me my application was ok, but it was missing 1 letter from my last name 😅

LOL, apply right away and loose the money again?

First find out WHY your application is denied, get the correct documents and than apply again using them.

You can apply right away, best to review your application first, seek a second opinion on it to try and find out why you were rejected

you can reapply right away. However i do not recommend you reapply from the same embassy because it will be the same set of staffs who rejected your application that will be reviewing your new application again. If you reapply with all same docs with the same embassy it is high chance that you can get rejected again