If you only want the files non-recursively in the current directory, combine what you have:
read -p 'Enter the directory path: ' directory
for file in "$directory"/*; do
echo "$file"
done
If you want to loop recursively and you have bash 4, it's not much harder:
shopt -s globstar
for file in "$directory"/**/*; do …
But if you only have bash 3, you'd be better off using find
.
find "$directory"