logz.io is described as 'Real time, actionable insights into your log analytics data with ELK as a service'. There are more than 25 alternatives to logz.io, not only websites but also apps for a variety of platforms, including Linux, Windows, Mac and Self-Hosted solutions. The best alternative is Grafana, which is both free and Open Source. Other great sites and apps similar to logz.io are Prometheus (Free, Open Source), Sentry (Freemium), Kibana (Paid) and Datadog (Paid).
Prometheus is an open-source systems monitoring and alerting toolkit originally built at SoundCloud. Since its inception in 2012, many companies and organizations have adopted Prometheus, and the project has a very active developer and user community.
Datadog is a monitoring service for IT, Dev & Ops teams who write and run applications at scale, and want to turn the massive amounts of data produced by their apps, tools and services into a unified view of IT infrastructure. 120+ Integrations!.
Graylog is an open source syslog implementation that stores your logs in Elasticsearch. It consists of a server and web interface written in Java that accepts your syslog messages via TCP or UDP (or GELF messages) and stores it in the database.