The Cheapest Seats are the Best Protected
There are not many covered seats at Great American Ballpark, but some of the most well protected ones will be located at the very top of the 500 level as these seats are underneath a roof which sits atop the stadium. The seats with good coverage in the 500 level will be found in rows R-V in sections 520-537, and rows N-R in sections 509-519.
Lower Level and Club Seat Options
The last 3 rows of sections 127-134 (along the first base side) will also have decent coverage from the overhanging seating deck above, and you may also want to consider the Club Seating options which will give you access to a private club lounge where you can get out of the weather.