If I understand correctly, you're looking for Postgres hosted as a service? Heroku provides hosting as a service [1], and we do allow you to connect from anywhere. It's true that generally folks in the Postgres community prefer to run databases with perimeter security and only leave your database directly accessible to your application, but we've never had any problems and we are confident in our security configuration. If you find our plans are not a good fit, you can find a list of other vendors on postgresql.org [2] (though I'm not sure which provide databases directly accessible from the public Internet).
