Summary of editorial
The exercise bars and equipment are on Roosevelt Island next to the Octagon soccer field, across the river from Manhattan. You can take the F train there and walk (or catch a RIOC bus, which is free as of this post). Or you can come over to Roosevelt Island from the Queens side via the smaller bridge. The exercise bars are west of the large soccer field and a garden area.
Here there are places to do pull-ups, dips, core exercises and more. There are also some easier equipment like the Tai Chi spinners for people wanting to take it a bit easier.