Facebook's Insights data can provide some of this information. Just go to
http://facebook.com/insights and data will come come for any pages that you admin. It will give you demographic information about your fans, the country, state and city they come from, gender, etc. But it will only give you aggregate info. It doesn't give you a breakdown by fan.
You can also download demographic and interaction data into excel to look at it by date. The Interaction data can be very interesting so you can determine what types of content your fans like and don't like by seeing how much they interacted with your post that day or how many page views you received that day. Track your overall engagement score to see how your doing on engagement. Increased engagement can increase your Edgerank score which relates to how often or if your page will show up in your Fan's Newsfeed.
You won't get time of day or where they are coming from with Insights data. You can however add Google Analytics to any custom pages or to your Wall. This post will tell you how:
http://www.socialmediaexaminer.com/h...book-fan-page/