What's the Best Social Listening tool in the market?

Well, it depends on a few different aspects such as the pricing plans or a variety of features a tool can provide. You'll find tools that are free but lack some functions that can be found within paid tools. Speaking of the latter, there are those quite affordable, ranging from $30 to a few hundred per month, but also those that will cost an arm and a leg. The good thing is that all the tools offer free trials or product demos so you don't have to pay up front for something you might not be satisfied with. You should also remember that each tool comes with its own set of pros and cons and there's no a perfect tool that could give you any features you could imagine.

It can also gives some useful daily/weekly stats on your site visits and visitors, if you connect it with google analytics.

The best I ever used when working for an agency was Crimson Hexagon. But of course it depends on your specific use case

Syften will provide you with Social News sites monitoring. It has more advanced filters than the alternatives.