[cbf]

But routing traffic via DNS change to different data center isn't the best approach as some ISPs cache DNS and would still send traffic to old data center.

All resolvers cache records for the TTL (or SOA minimum for negative lookups) specified by your authoritative servers.

A solution to this would be to have a round robin DNS to different data centers but that is still plagued if one data center develops a network issue.

If the clients are web browsers they will try the alternative addresses in a record set if the one they pick doesn't respond.