Question

would you expect the N-O bond in HNO2 to be longer, shorter, or the same length as the N-O bonds in NO2^-

Answer 1

Longer, this is because the H in HNO2 is bonded with an oxygen, no longer allowing this structure to have a resonance structure.
NO2 on the other hand has one double bond and one single bond, so it has a resonance structure. And resonance structures are actually one structure so there isn't really a single and double bond, it's actually a 1 and 1/2 bond that calls for a higher bond order.
And I higher bond order will result in a shorter lengths!
I hope this helps out!!! And just out of curiosity, is this off of an AP FRQ packet??