Most domain reseller provides a free DNS. Most of them works pretty well in terms of UI and update time (e.g. NameCheap), but some are less so (e.g. NameSilo).
You could use Cloudflare DNS on the Free plan.
NOTE: Before Cloudflare I use Amazon Route 53, which cost $0.50/month per domain, and additional query cost ($0.400 per million queries).
Sigin into Cloudflare, at Home click Add Website (or click Add site at the top bar), select a Free plan and update your domain's nameservers to Cloudflare.
adrian.ns.cloudflare.com
ken.ns.cloudflare.comCloudflare will auto import existing DNS entries. You can configure each Type A or CNAME to use Cloudflare DNS only (Grey Cloud symbol at Status column), or use Cloudflare DNS and HTTP Proxy - CDN (Orange Cloud Symbol).
NOTE: I usually choose DNS only (Grey Cloud), mostly because the Free plan have limited configuration of the HTTP Proxy (a CDN cache system to faster page load) and I do not want to use Cloudflare SSL.