In genuine Bortle 3 skies (meaning that you can see the Milky Way with ease and in detail), through an 8-inch scope, the spiral arms of a half dozen galaxies are pretty obvious -- once you know what to look for. Figuring out what to look for and training my eye to do so took me about two or three years.
At this time of year, M33 is your best bet. But it's tricky; the spiral arms are huge but not terribly well defined. Anyway, while engaged in the relatively easy task of observing all the nebulae and star clouds inside M33 that have NGC numbers, think carefully about how they all hook up, and see if you can discern some structure to it.
In late winter or spring, M51 is by far the easiest galaxy for a northern novice to spot spiral arms. M51 has much higher surface brightness than M33, and the arms are much narrower and sharper.
In all cases, I found that the trick is to look not for the arms themselves, but rather for the dark spaces between the arms.