Sharing drives between multiple sites

I've been tasked with finding a solution to allow us to move away from using terminal servers to accomplish drive sharing between multiple sites. Users complain that the terminal server is slow and inconvenient. What would be the best way to accomplish what the terminal server does across multiple sites to allow users access to multiple shared drives with permissions?
I appreciate any advice!

Are the sites all on the same domain? Why do they need terminal servers can't they just map the network drive to their computer? Are the sites across the country or not connected via high speed to the Datacenter where the storage presumably is?

There is no domain setup right now. If I setup a domain, would it be easy to share drives between multiple sites? All the sites are in the same state. They all have high speed internet.