Been to Silver City many times, both the easy way and harder ways. Since you asked for the easier way, here ya go: After you pass through Murphy on hwy 78, look for the Silver City turn off. I believe Silver City rd is paved for several miles. Near the end of the paved portion, there is a trailhead parking type area. From there just take the main rd up and over New York summit and head to SC. Couple of side trips: before you turn left towards SC, there is a dirt road which leads up to War Eagle Mtn. There is some fairly easy riding once on the ridge, but there are a few tricky spots on the way up. Also, the trail up to the top of War Eagle is a little tricky, but you can bypass this and stay on the ridge. If you go this way, you'll probably want to stay on the ridge as some of the trails that go downhill turn into a real bugger. At some point turn around and depart the way you came in (easiest).
Another option is to stay on the Silver City road passing up SC and head towards Jordan Valley. Fairly easy riding here as well and hard to get lost. Watch for Rattlers anytime you get off the bike this time of year.
Taken 7-8 years ago, but found this along the way up to War Eagle
On top of War Eagle looking down on Silver City
Get rugged on the south side of War Eagle and you have to be careful for mine adits, but there can be some rewards
(Added: I should also mention, which is what I really meant, there are numerous "Vertical" shafts as well. In this area I've seen some of these vertical shafts open and dangerous,
while others have been blocked so we don't accidently fall in.)
If you don't end up going soon, I'm hoping to ride up there late July or early August. Good luck and have a fun ride.
P.S. and don't forget to take lots of pictures.