The easiest place to host your DNS records is the registrar at which the domain name is registered. However, few registrars (if any) offer the features and flexibility found in quality DNS Hosts (services that specialize in hosting DNS records). And none can come close to offering the many benefits available at Cloudflare.
Cloudflare includes tools that can make your life difficult if you're not well versed in the technology, so I suggest a little caution. However, the service is very well documented and extremely well supported. As long as you are willing to dig into Cloudflare (or hire someone who can handle it for you), this is absolutely the place to host your DNS.