Free or Trial Analytic Tools You can Use

Web

• Google Analytics
• Open Web Analytics
• Yahoo Marketing Dashboard
• Piwik
• Clicky
• GoingUp
• Stat Counter
• Site Meter 

Social

• TweetReach
• Social Mention
• Twazzup
• HowSociable
• Reachli 

Web & Social

• Reinvigorate
• MixPanel
• Woopra
• Addictomatic
• IceRocket

You can also use a lot of the same tools that were used for your digital audit [here's that blog post to help you remember those]

Conducting a Digital Audit

Here's some tools for conducting a digital audit:

• Google Webmaster Tools http://www.google.com/webmasters/tools/
• Hubspot’s SEO Audit Tips http://blog.hubspot.com/blog/tabid/6307/bid/34088/How-to-Audit-Your-Website-for-Improved-SEO-and-Conversions.aspx
• Woorank SEO and Traffic Estimator Report www.woorank.com
• Inbound Link Assessment, SERP Results www.moz.com/tools
• Other Useful Google Insights Tools: https://support.google.com/webmasters/answer/156184?hl=en
• to check inbound links on Google: link:url.com
• Sitemaps: https://support.google.com/webmasters/answer/156184?hl=en
• Domain Name Search: domainsatcost.ca
• Link Checker: brokenlinkcheck.com 
• Mobile Analysis: http://mobitest.akamai.com/m/index.cgi

The complete digital marketing audit checklist can be found here >>