If you are going to get a new Wi-Fi router, then everything should be simple. Just pack it up at the old place, get to the new place, set up the new Wi-Fi, set up the hub so it’s using the new Wi-Fi, and then physically deploy all your devices using the usual best practices. you shouldn’t have to change anything about your hub connected devices (Zigbee, Zwave, or thread). wi-Fi devices will have to be changed to the new Wi-Fi network.
A Guide to Wireless Range & Repeaters - #11 by JDRoberts
If instead you are taking your old Wi-Fi router with you, that’s both good and bad. The good is that you don’t have to change the Wi-Fi credentials on anything. The bad is that it may take your Internet provider 4 to 6 weeks to update the physical address associated with your Wi-Fi SSID so your presence in Smartthings may be off until that is updated. This has nothing to do with smartthings, it’s just the way Geopresence works in most countries.
Weird things happening with smartthings since we moved
But other than the presence issue, it should be pretty straightforward. 
One thing to note: since you said, you weren’t taking all the devices with you, if you are leaving behind any means, powered the wave or Zigby devices, it’s possible you won’t have enough repeaters in the new place and you’ll need to get a few extras. But you’ll know that soon enough since devices might be unreachable.