Ask HN: What's the best solution for GeoDNS that supports failover?

I have some requirements but I'm struggling to find an affordable solution that does all of them.

I have two web servers, and would like to use GeoDNS with them, so that users are always connecting to the nearest/lowest-latency server. Additionally, if one server goes offline, all traffic should be directed to the remaining online server automatically.

Basically I'm looking for "Failover GeoDNS". There are plenty of Failover DNS services, and plenty of GeoDNS services, but not many that do both.

Does anybody have any suggestions? A do-it-yourself solution should also be fine as long as it itself is resilient.