Address geolocation is a hard problem. It requires deep understanding of address systems and reacting to ever-changing, real-world, messy scenarios.
For example, you could get a database of the Zip codes of the United States and their approximate locations, but it would only be a snapshot. You'd find over time that new Zip codes would be added and missing from your data, and that existing Zip codes had been expanded to include other areas. You'd also find many Zip codes that are "non-locatable", such as those used to send mail to military overseas. You could even find a single Zip code that has addresses in two different time zones.
Take international concerns into effect and you'll find all sorts of edge cases. Every country and territory has their own special rules and situations.
It is a problem worth paying a service provider for. Trying to do geolocation in an offline manner might be possible, but it isn't advised.
The second part - figuring out which time zone goes to a location, is also messy. However it's slightly easier to coordinate. The Time Zone Boundary Builder is the main open-source project that attempts this. Most libraries referenced here use that data. But even then, it has updates and relies on borders established by Open Street Map data. Some of those borders are in dispute, so a service from Google, Microsoft, or others could give different results because they have map data with different borders. If you care about such things then you might want to test some edge cases against the different providers to see if you're satisfied with the results. You may find that the TZBB data works well, or you might prefer one of the online solutions.
