From the second structure, it is clear that the central atom Nitrogen carries a positive charge, while two of the three oxygen atoms carry a negative charge each. But from the structure of Nitric acid from which Nitrate ion is formed, Hydrogen atom is bonded to one of the oxygen atom, while Nitrogen donates a pair of electrons to one of the other two oxygen atoms and engages in double bond with the other. Will this mean that the structure of nitrate ion due to removal of a Hydrogen atom from nitric acid be structure 1?
Your II option and Anga's answer are my preferred choice. Also, Erik Rakovsky makes an important point about the N-O bond distances as well. Coordination of nitrate to a metal can modify both the sigma- and pie-bonding of the nitrate group on coordination, thus, changing the N-O bond lengths. Addison et. al. published an excellent review on structural aspects of coordinated-nitrate complexes: http://pubs.rsc.org/en/Content/ArticleLanding/1971/QR/qr9712500289#!divCitation
We published a recent chapter on NOx (NO, NO2, NO3) isomerization and looked at how coordination affects mode of binding of NOx : http://www.sciencedirect.com/science/article/pii/S0898883814000117