Grayling are a hoot. As Bill says, most of the rivers in the far north have them. Find fast water and you're usually into grayling pretty quickly. Anyplace where rivers flow into or out of lakes usually has loads of them.
Easiest way to catch grayling is with an ultra-light spinning outfit and little spinners .... size 0 Mepps or a little Panther Martin is very tough to beat. Small hair jigs are also good. Don't bother with twist tails up north, they get destroyed quickly and are more fuss than they're worth. You'll catch just as many fish on hair jigs, and they're far more durable. Size matters more than anything else, so nothing bigger than you would throw for crappies. Fortunately, grayling aren't exactly shy, so you don't need to make long casts.
To my mind, the best way to catch them is to fly fish with small (size 10 - 14) dry flies (any colour). The way grayling crush floating flies is just incredible, they're some of the most ferocious topwater hits you'll ever see in your life! I'm not a big fly fisherman, most days I can barely make a cast without hooking my own ear, but it's so much fun that's become pretty much the only way I fish for grayling now. It's easy, and it's a riot. A basic 5-weight outfit you would use for stream trout down here works just fine, and if you can cast even 15 or 20 feet then you're good to go. I became completely enamoured with grayling at one point and built a 6-foot, 3-weight G Loomis just for them. It works great - at least until a lake trout comes along (yes, they will also hit small dry flies at times) so the heavier outfit is probably more sensible overall.
Most grayling you catch will be around 12 to 14 inches. Anything around 16 inches is a really good fish, and one over 18 is a monster. They fight like a whitefish, except that they're in fast water so it's a lot more intense. When they extend that big dorsal fin in the current it's like someone opened an umbrella underwater, and the fish just suddenly takes off on you. It's not unusual to have to chase the bigger ones downstream, especially when you're fishing in strong currents.
Finally, grayling are superb eating fish, especially fresh-caught and fried up for shore lunch. Eat the average-sized guys and release the big ones.
This picture is from my first-ever grayling experience in Manitoba, many years ago. We kept two fish for a shore lunch, and I wanted a selfie. With one hand on the camera, what's a guy to do? I will say it was a lot more rewarding about 20 minutes later after the things got cooked.
Go do it - those northern trips are pricey but you will remember the experience for the rest of your life.