Hi,
One option would be to use nslookup to determine the region. For example, say the target key vault url is mykeyvault.vault.azure.net, you could use command prompt and enter below command:
nslookup mykeyvault.vault.azure.net
In the output, you might see something similar to below:
Name: azkms-prod-wus-b.westus.cloudapp.azure.com
Which would let you know that it is in region West US.
Please click Accept Answer and upvote if the above was helpful.
Thanks.
-TP