Method to find the statistically significant clickthrough rate of several groups with no control I have basic data that looks like this:
Group    Visits   Clicks
A        2029     186
B        2340     171
C        2780     176

And I'm trying to determine whether one of the clickthrough rates (Clicks / Visits) is statistically better than the rest of the clicks. I have tried using a Chi Squared test to determine that these groups are in fact different, but am then stuck as to how to determine the 'best'. By eyeballing the numbers I can see that A is the best clickthrough, but is there  a test that would show this absolutely?
 A: (I'm assuming you had a significant $\chi^2$ test, which is not explicit in your question)
Why do anything other than interpret your data in light of your model? Could B or C possibly be best, based on your data?
You could just test for subsets. Do a $\chi^2$ containing just A and B, and then do one just containing B and C. What if they're not significant? Then what would you conclude? What if you get significant effects but they go away when you correct for alpha inflation? Then what do you conclude? What if you find A is not different from B but B is different from C? Would you really want to say A and B are equal? There are myriad questions, many of them problematic, that can stem from further testing when you've already asked a question and received a perfectly adequate answer.
Your question is that click versus not click depends on group. You did a test of that. Interpret the results you have to mean something because, according to your test, they likely do. I'd just say:
"I tested whether clicks depend on group,  $\chi^2$ = xxx, p = xxx. The best rate was A with 9.2%, followed by B with 7.3% and C with 6.3%."
If you want to do something more interesting and potentially useful, don't just report tests but report estimates and confidence intervals. You can generate confidence intervals around your probabilities of click. You could look this up on the internet or use the binom package in R, which can perform any of the methods (or just use the one given in binom.test, which is conservative).
