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If you have a Free ISP, where such information is not made public to you, I'm not aware of a way that you can find out, as most of the "other" tricks like clever PHP will not be available to you.
The "fresh date" (the date in green) in the Google results for your site (try allinurl:www.yoursite.fiddlybits) will tell you which pages have been visited in the last two days or so. (After that the dates will vanish)
Yep. It'll all be in the logs. And Googlebot is a nuisance. For whatever reason, it is frequently all over a couple simple amateur sites I run. I used to think Google didn't trust me. I've concluded that Googlebot is just hungry, and this is her way.