It depends on your NSX setup, do you connect the VMs to NSX VXLAN logical switch networks or to a VLAN-backed PortGroup provided by the physical switch?
If the VMs are connected to the NSX logical switch networks you can extend the logical switch to multiple sites but you would need cross-vCenter NSX setup - https://blogs.vmware.com/networkvirtualization/2016/03/cross-vc-nsx-multi-site-solutions.html/
Additional note, if you need to have layer-2 adj between logical switch and physical network which can be achieved through layer-2 bridging, this feature is not supported in cross-vCenter setup
If the current NSX setup is not setup for cross-vCenter, you would need to perform some changes and probably some virtual/logical network migration within NSX.
Please note NSX does not do any ingress routing optimization so even if you can do local egress optimization in NSX, you would need to handle the north-south ingress routing outside of NSX.
If the VMs are connected to VLAN-backed PortGroup then you would need to rely on physical network switches to extend the subnets such as using VXLAN, OTV, EVPN or something else which typically need a compatible set of physical switches.
Extending layer-2 between sites normally a complex setup esp on the ingress routing and when you have stateful services like LB or firewall. This blog post might give you more idea about it: http://blog.senasosa.com/2017/01/dc-ingress-traffic-with-stretched-layer.html
