How to modify local contrast of a photo in Lightroom 4? The only thing comes into my mind is to use the brush tool. Is there any other way to achieve this or a plug-in to let me modify the local contrast of part of the image?
I'm not a Lightroom user (often), so I'm not overly familiar with what's available natively, but you might find a plug-in like Topaz Adjust 5 to be just about the right size and shape of ticket. It works from within both Lightroom and Photoshop (and any PS plug-in compatible editor, as well as a standalone with a free lightweight host), and offers both global and local adjustments. The ability to paint effects in and out is, I think, a deliberate nod to the environments that won't allow you to play with layers in the host program.
(No affiliation—I'm even deliberately avoiding the affiliate program—just a very satisfied user.)
Clarity Adds depth to an image by increasing local contrast
From Adobe's site.