Here is a nice alternate route to Leakey from Medina if you want to skip RR-337E. Unfortunately, it will add 20 miles to your trip. We have been taking it when we don’t feel like going 10 mph through the sharp curves with lots of gravel on RR-337E. In the picture below, we stopped for a break on RM-1050.
The detailed route is shown below:
From Medina, TX, head south on TX-16 S. Go 8 mi.
Right on RR-470 through Tarpley. G0 17 mi.
Left onto RR-187. Go 3 mi into Utopia.
Right onto RR-1050. Go 14 mi to US-83.
Right onto US-83 N. Go 9 mi to Leakey.