Here are some of my favourite tools for web perf and analytics:

Monitoring

Uptimerobot.com - Free tier. 50 monitors. Sends a request every 5 minutes to a website.

Pingdom.com - Free tier. Gives average response times.

Azure have an excellent uptime monitor inside Application Insights

Infrastructure

Builtwith.com - eg is this a wordpress site, what webserver etc..

Deadlinkchecker.com This handles redirects well

Performance

Apache benchmarks load testing from the command line

Web Accessibility

Guidelines
Chrome extension