Which atoms in a given amino acid are able to form hydrogen bonds with water?
The positive end of water can hydrogen bond with N, O, or F, as you said, but only if A) the geometry of the atom allows the water and N/O/F to get close to one another and B) the N/O/F has a lone pair of electrons.  This happens at each of the green circled nitrogen and oxygen atoms.  The red circled nitrogen is a decoy, as it is neither geometrically available nor does it have the appropriate configuration of electrons.

The negative end of water can hydrogen bond with hydrogen atoms that are attached to the N/O/F atoms, including the ones that are attached to the N atom that was not correct for the first part.