How to record unique hits in node counter stats?
Node view count

You may want to use the Node view count module for this. Here is a quote about it (from its project page, bold markup added here):


  ... allows to count node views. Unlike statistics module, this module records each view of node with user uid and timestamp. So now you can know how many times a user viewed node by day, week, month and etc.
  
  This module is integrated with Views module. You can use it to create different statistics pages, output new not viewed nodes for user and many more.


Specific to the D7 version of it, this is what is included also on the project page:


  Also now we count node views for anonymous users.


Statistics Advanced

Be aware of the  Statistics Advanced (*) issue "Port Statistics Advanced Settings to D7", with current status = needs review.

My "recommendation" for anybody looking for a D7 version of it, is to review what is attached to Comment # 55 in that issue. And report any potential deficiencies in that same issue (confirmations that it works fine would be appreciated too, also via that same issue).

Other modules to consider

If the Node view count and/or Statistics Advanced (*) module doesn't fit your needs, then you may want to consider reviewing this shortlist of possible alternatives (quotes are from their project pages).


Visitors (*):


  Displays information about visitors, and integrates with the WhoIs Lookup module

Better Statistics:


  introduces a Statistics API, which allows for a way to collect, limit, and route custom access statistics and data.

Piwik Web Analytics:


  Adds the Piwik web statistics tracking system (free open source) to your website.
  
  Related module: Piwik Reports, which provides graphical reporting of your site's tracking data inside Drupal.

Chartbeat:


  ... to provide third party integration with Chartbeat, for real-time site monitoring statistics.

Stat Counter:


  ... provides an integration between Drupal and StatCounter web statistics.



Enough options to "explore"?

Disclosure: I'm the maintainer of the modules marked with (*).