Totally you must consider following daily tasks in VI administration:
Look at the events, warnings and any prompted required actions in vSphere client or web client when you are connected to the vCenter Server.
Analyze more detail of log files if any special incident has been occurred and you saw in step1.
Monitor performance of cluster's nodes and critical virtual machines in your environment. Also consider status of free resources in the cluster, specially computing resources (processor and memory)
Control operation of each daily and weekly VM backup job and check the status of VM, before & after running the backup task if it's happened in work hours duration. Also control state of snapshot files and *.vmdk files after the backup job completed.
Control status of vCenter server and other related solution that is connected to the VMware vSphere like Horizon View or any vRealize services.
Check the operation of DRS recommendation and HA agent status of the ESXi host clusters
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