If you want to direct users to the closest server to them using only DNS then i would recommend setting up a couple of cheap VPS's you can use to host your own DNS in different geographical locations.
DNS round robin isn't really a great way to do geo location based load balancing because if you have multiple A records with different IP addresses the DNS server will merely alternates the order of the address records each time a name server is queried.
Therefore you could have a DNS server in North America resolve your A record to your web server in North America while having your DNS server in Europe resolve your A record to your web server in Europe. (These locations are just an example, the point is having your DNS servers resolve your A records to your web server that is closest to that specific DNS server)
This is because a client should be using the DNS server that is closest to them, you can read more about how a client chooses the closest/fastest nameserver to use here - https://superuser.com/questions/527116/how-does-my-browser-locate-the-nearest-dns-root-servers
This should give you the outcome you desire while only using DNS servers but there are load balancing commercial services that exist that would be a lot more elegant.