For one of the website I am managing their hosting provider says there were 250,000 hits in a 5 day period last month and I am not seeing it with Google analytics. They are saying that perhaps someone is trying to hack that website. Again, I am not seeing any of that. How would I be able to check on that? Are there any kind of tracking system I can use that better at catching these than Google Analytics?
Google analytics will only record hits if they are hitting a web page having your analytics code embedded in. However, if they are hitting some other port (other than port 80/443), or if they are directly hitting your IP on port 80, there's a big chance that analytics won't record those hits. So, ask your hosting provider to send you some logs of this hits and post them here. We can then decipher it further.
Check the error logs for more information and check access logs for 'POST' and 'GET' function , it will help you to resolve hacking issue because most of the hacker use 'POST' and 'GET' function to hack php pages.
Check error log from your Hosting account C panel , get info about your website is ok or is getting some trouble.
If your ordinary web page has 100 images, then every visitor produces 100+ requests when only one of them registered by GA. So, real "humen" traffic could be significantly lower for 250K hits monthly. Do your pages contain a lot of images?