There is a homeless shelter and a mental institution on Randalls island. many of the wino's you see are people that are going to that homeless shelter. in my experience, they are more interested in drinking and smoking crack (literally, I've seen it) than anything else. Depending on what part of queens you live in you can take the QBORO bridge. if you live in astoria it probably adds about 6 miles onto your trip though.

Oh yeah, you can also go over to randalls island via the 103rd street bridge on the east side bike path. that path is usually free of weirdos then you just have to go over the triboro portion to queens. I find the section of triboro that comes into manhattan at 125th is the part that is always filled with crackheads. Be advised that the 103rd st bridge crossing closes down for the winter on Nov 1st and doesn't reopen until March.