As somebody who has used Nike+ since it was introduced in 2006, I feel your pain. There's no reason (other than greed) they should have removed the ability of iTunes to sync the iPod data to the Nike+ servers.Also, iTunes 12.7 not longer sync's Nano run data with your Nike+ account. Nike suggests using an Apple Watch - using Nike Run Club app on my iPhone.
You could retro install iTunes to prior to 12.7 but that introduces other issues.
So to track my runs as my Nano has seamlessly done so for years, Apple (and Nike) is forcing me to buy a Watch. It's hard to view this cynically – forcing me to buy more Apple stuff. I refuse to carry my iPhone while running - for several reasons. This reminds me of the time AT&T and iTunes simultaneously stopped supporting the original iPhone about 4 years after launch.
The lack of support for syncing is "due to music and data management that has improved considerably over the last few years and iTunes no longer supports this older technology." ...I'm sure it could if they wanted it to.
While it's not actually necessary to have your iPhone with you when using the Apple Watch for Nike+, I personally can't recommend that solution. I eagerly bought the Nike+ version of the watch, and the experience with Nike app has been miserable. It crashes frequently, and really struggles with workouts longer than about 10K. Ever since buying the watch, I've had to manually enter my workouts more than 50 percent of the time due to the fact that the Watch app failed to sync them automatically. In fact, they simply disappeared from the watch (and iPhone app) altogether.
I hope you figure out a solution so you can continue using Nike+ (if that's what you want to do). Me, I'm thinking of finally ditching Nike after all these years.