Hi Canuck - I keep a Yam WR250R in Cave Creek, which is north of Scottsdale. I'll give you three day trips to get your feet wet:
1. Bloody Basin Loop - Ride north on Scottsdale road to its end at Cave Creek Road. Turn Right onto Cave Creek Road. Follow it east and north. It will quickly turn to dirt once climbing out of the valley. It changes name to Seven Springs Rd. Follow to its end at a T intersection with Bloody Basin Rd. Turn right to go to Sheeps Head Bridge (or something like that). It ends on the Verde River. Turn around and ride west on Bloody Basin Rd. West of the Seven Springs intersection it climbs out of the Bloody Basin to a plateau called Agua Fria National Monument. You end up on I-17 for the ride south back to Phoenix...or ride back the way you came.
2. Crown King - You can get to Crown King either by continuing under the I-17 above (by following Crown King Rd) or from Black Canyon City further south off of the I-17. Find Black Canyon City on I 17 and look for Maggie Mine Rd. on your right. Take Maggie Mine north to intersect with Crown King Rd. Continue north on Crown King Rd past Bumble Bee to Cleator. Note the Blue Bell Mine Rd on the right at Cleator. You'll want to ride that later. It goes to Mayer. Slightly more technical.
Anyway, continue climbing up the Crown King Rd to Crown King and have lunch. Eventually you'll want to find the Senator Highway in Crown King and take it to Prescott. Maybe save that for another trip. I have not done that yet. Let me add that all through this area is some great dual sport riding, but it can get very tough quickly so you should be with experienced friends if you want to explore the off shoot paths off the Crown King Rd. Also, there is a back way to Crown King from Lake Pleasant too. I'm going to try that this winter, but I need tracks I think, if I do it solo.
3. Four Peaks Rd/A Cross Rd Loop - Take the Bee Line Highway north (87) from Fountain Hills. Keep a sharp eye out for Four Peaks Rd, which will be on your right. You'll see the Four Peaks on the skyline as you approach it. Four Peaks Rd will take you over those mountains at the north shoulder of the northernmost peak. It will take you down the other side and deposit you at the north end of Roosevelt Lake on Hwy 188. Turn right onto 188 for a few yards and turn left onto A Cross Rd.
You'll come upon a large water crossing, but it is shallow and cars use it all the time. A Cross will take you around the north shore of the lake and deposit you on Hwy 288. 288 is dirt north up the Mogollon Rim; or paved south toward Globe. You pick you route back from there.
These are easy dirt roads for a bike like yours, but they are slow and full of babyheads and such. Very scenic! Even remote in sections. Mud can make sections impassable too. You'll know pretty quickly because it is that slime stuff that makes it hard to even walk in.
My suggestion is to get a DeLorme Atlas and Gazetter map book for Arizona. It has good detail for the many dirt road opportunities throughout Arizona. Also, get a GPS that will take tracks. I have Garmin 60Csx, but there are newer ones like the Montana that are much better. You really want tracks because people share track files for their dual sport rides. Routing isn't very useful for much of the remote stuff. Anyway, tracks allow you to plug and play trips that others have already ridden.
My favorite part of the world...