There're a couple of ways to achieve this using REST API. Basically this kind of information is only available to System administrators:
1) Using query service: you can use the query named 'adminVM':
GET <host>/api/query?type=adminVM
This returns a list of AdminVMRecord objects with a 'hostName' property in them. This 'hostName' property contains the IP address of the ESX host on which the VM resides:
<AdminVMRecord vmToolsVersion="6404" vdc="https://10.26.49.174/api/vdc/94964469-f3da-4f11-ae77-321f07421f83" vc="https://10.26.49.174/api/admin/extension/vimServer/e6136146-e097-42b6-a282-12d1967a92c5" status="POWERED_OFF" org="https://10.26.49.174/api/org/73ab2eb6-802b-46a6-8a3d-e55a0a99a957" numberOfCpus="1" networkName="AutomationNetwork" name="TemplateNic" moref="vm-1504" memoryMB="32" isVdcEnabled="true" isVAppTemplate="true" isPublished="false" isDeployed="false" isDeleted="false" hostName="10.23.116.201" hardwareVersion="7" guestOs="Other (32-bit)" datastoreName="datastore1" containerName="TemplateNic" container="https://10.26.49.174/api/vAppTemplate/vappTemplate-9e540670-44e9-45a0-950d-1dae5b9d198b" catalogName="CatalogvappTemplate-9e540670-44e9-45a0-950d-1dae5b9d198b" href="https://10.26.49.174/api/vApp/vm-05f2a7c5-016b-4043-81dc-d217b4a6583f" pvdcHighestSupportedHardwareVersion="8" containerStatus="RESOLVED"/>
2) Using the VCloudExtension element inside VM representation:
GET <host>/api/vApp/vm-<uuid>
This returns a <Vm> object with <VCloudExtension> element inside. It contains information about host, datastore and actual VM in vCenter. The drawback is that it returns the morefs (VC IDs) of these objects so you'll have to make another API call to resolve those IDs to IPs.
<VCloudExtension required="false">
<vmext:VmVimInfo>
<vmext:VmVimObjectRef>
<vmext:MoRef>vm-1504</vmext:MoRef>
<vmext:VimObjectType>VIRTUAL_MACHINE</vmext:VimObjectType>
</vmext:VmVimObjectRef>
<vmext:DatastoreVimObjectRef>
<vmext:MoRef>datastore-79</vmext:MoRef>
<vmext:VimObjectType>DATASTORE</vmext:VimObjectType>
</vmext:DatastoreVimObjectRef>
<vmext:HostVimObjectRef>
<vmext:MoRef>host-78</vmext:MoRef>
<vmext:VimObjectType>HOST</vmext:VimObjectType>
</vmext:HostVimObjectRef>
<vmext:VirtualDisksMaxChainLength>2</vmext:VirtualDisksMaxChainLength>
</vmext:VmVimInfo>
</VCloudExtension>
Regards,
Todor Todorov