You must define variable night outside of the while loop, like this:

[...]
let night
let isValid = false;

while(isValid == false) {
    night = Number(window.prompt("pick a night"));
    if(typeof night == 'number' && night >= 1 && night <= 8){
        isValid = true;
    }
}
 
document.write(night);
[...]

let is a block scope variable i.e. it will only be accessible in the while loop. If you want to access it outside the while loop, declare it as a var variable which is a global scope.

To be honest, I wouldn't even recommend using a while loop.

Also, one issue with your code is that you are checking if typeof night === 'number', but it will always be number since you wrapped the value in Number(). NaN itself is of the number type.

<script>
    const getNight = () => {
        const night = +window.prompt('Pick a night:');

        if (isNaN(night) || night < 1 || night > 8) {
            alert('Try again.');
            return getNight();
        }

        return night;
    };

    document.write(getNight());
</script>