Western Union has offices in almost every country and so the opening and closing time of Western union may vary depending on your location. However in most countries, Western Union opens at 9 AM and close at 5 PM.
It should be noted that in most countries, Western Union doesn,t have a specialized office (building) for running their business. They run their business in connection with banks and tend to rely on their time schedule. So a western union office operating in a bank that closes at 3PM, will also close at 3 PM. In otherwords the easiest way to know what time Western Union offices in your country close, is to find out the closing time of most banks in your Country (location).
In countries where Western Union has specialized building for running their business, their office are open 24 hours.