This morning Monkey Cage mentions a new study of economists that shows that economists who blog are significantly more likely to be regarded highly by their peers than other economists.
My guess is that this is probably doubly-so for graduate students, with the important caveat that it is very difficult to do an academic blog well before you have had some training. If you want to see some excellent political science grad student blogs, check out Will Winecoff, Rachel Strohm, Dan Trombly, and Shelby Grossman.
And if you want to see some of the best blogs in political science, I highly recommend Monkey Cage, Seth Masket and Jonathan Bernstein in American politics, and Dan Drezner and Duck of Minerva in IR, and Jay Ulfelder and Chris Blattman in comparative politics. Ulfelder is particularly a standout – he brings up interesting research and new datasets all the time.