The U.S. Postal Service provides a suite of USPS Web Tools that can be used to validate or find mailing addresses, track and confirm mail delivery, calculate shipping rates, and create domestic or international shipping labels.
The Domestic Mail Service Standards APIs can help predict when a package will arrive at its destination. APIs are available for Priority, Package (which includes Standard Post Bound Printed Matter, Library Mail and Media Mail) First Class, and Express Mail types. The USPS reiterates that these are predictions, or standards, and not guaranteed dates.