PJN from Overland Park, KS on 9/1/2021 12:07:35 PM:
Yes, you can see Crazy Horse from the trail. It is not a great, up-close view, however there is signage next to a vantage point. Crazy Horse is located at the crest of the hill between Hill City and Custer. If your goal is to see Crazy Horse, then I would immediately turn around and return the (approximately) 9 miles downhill to Hill City and stay there. Several lodging options, just google and you will find a number of selections. The other option would be to continue downhill about 6 miles to Custer and stay there. Just be aware it's over 60 miles each way from Deadwood to Custer - thus my recommendation about staying in Hill City.
I recommend not bicycling Needles. Very curvy and narrow indeed.