For some reason, Google Web History no longer has a way to navigate to a certain date, at least not from the UI. Fortunately, you can change a URL parameter and go to a certain date. Here's how to do that:
1. use the Unix epoch time converter. Scroll to the "Convert date to epoch timestamp" section, enter the date, enter 0 for hours, minutes and seconds and then click "Convert". You'll get a number like 1305072000. This is the number of seconds that have elapsed since January 1st 1970.
Copy the value you've obtained and add six zeros to convert the number from seconds to microseconds. For example, 1305072000 becomes 1305072000000000 (this corresponds to May 10, 2011).
2. go to https://history.google.com/history/lookup?st=web (you may need to sign in)
3. add the following parameters to the Google Web History URL:
<s=MICROSECONDS&fts=MICROSECONDS
You'll need to replace MICROSECONDS with the value you've obtained previously. For example:
<s=1305072000000000&fts=1305072000000000