Datadog is not available as a self-hosted solution but there are plenty of alternatives for power users and business that want to host a solution on-premise. The best Self-Hosted alternative is Grafana, which is both free and Open Source. If that doesn't suit you, our users have ranked more than 100 alternatives to Datadog and many of them are available as a self-hosted solution so hopefully you can find a suitable replacement. Other interesting Self-Hosted alternatives to Datadog are Zabbix, Netdata, Graylog and Beszel.
Zabbix does not work off of the StatsD / Graphite basis, requires an agent on each monitored instance (instead of sending simple updates via UDP, or HTTP), Zabbix cannot adapt to dynamic infrastructure environments.