If I understand you correctly, you want to achieve something like vSphere HA clustering, but for storage. So if a physical storage device (i.e. a NAS) fails, all VMs hosted on that NAS would already be present on the secondary NAS and all operations would automatically continue with 0 downtime.
I know there are ways to HA cluster NFS servers and storage, but I have never heard of anyone doing this with vSphere, and I would doubt it would be supported for VM storage. There may be a storage vendor who has a similar capability, but it probably requires a license and a purchase, like anything else.
Outside of that possibility, there isn't anything in vSphere to enable this capability, so you'd be looking at implementing the resilience in the hardware underneath. You can implement vSphere replication to replicate your VMs between storage locations in the same vCenter and cluster. This would not be an automatic scenario for failover.
If you wanted to add automatic failover, it would require SRM to orchestrate the failover, and you would still experience downtime during the failover. This would probably be overkill for a LAN scenario, since SRM requires multiple vCenters.
You could look at an array-based replication solution to replicate between the NAS appliances. I don't know what devices you have or if any utilities exist for that.
You could implement a backup solution to back up the VMs to the secondary NAS.
Both of those options will still incur downtime in the event of a device failure.
Lastly, you could look at using VSAN (extra license, and is not NFS), which will aggregate locally attached storage from your ESXi servers and create a logical datastore that spans all the servers. In this case if you lose a server or storage device, VSAN can automatically have copies of its components and objects spread around and be resilient to the number of losses you specify in the storage policy.
Other than that, you want to try to achieve the resiliency you're talking about by using devices that have redundant components such as multiple filers or storage heads, multiple network cards on each head, multiple disk shelves, multiple disks, etc. This way you can stand the loss of any single component without losing the entire device. You also should have multiple paths from each host to the device to ensure networking is not an issue.
