Determine structure from NMR
This is an interesting question. However, disadvantage is having only $\ce{^1H}$-$\mathrm{NMR}$ to deal with. Yet, it has pretty good resolution (probably using $\pu{400 MHz}$ machine) so we can resolve the splitting pattern very easily and predict the structure. 

First, OP has correctly assigned two degree of unsaturation. For molecular formula, $\ce{C5H9NO}$:
$$u=\frac{5\cdot2+2+1-9}{2}=2$$

However, OP's suggested structure was incorrect since chemical shift of -$\ce{OCH3}$ is usually greater than $\pu{3 ppm}$. Because of the chemical shift of -$\ce{CH3}$ group in the given $\ce{^1H}$-$\mathrm{NMR}$ is about $\pu{2.0 ppm}$, one can conclude that it is either olefinic or one $\alpha$ to a cabonyl group. Nonetheless, OP's suggestion of proton resonance around $\pu{6.66 ppm}$ is due to $-\ce{NH}-$ group is correct, but due to its deshielding nature ($\pu{6.66 ppm}$), one can suggest that it is an amido $-\ce{NH}-$ group. However, OP correctly assign it next to a $-\ce{CH2}-$ group.

Since I suspect non cyclic nature of the unknown, I have assigned splitting patterns and calculate relevant coupling constants assuming the spectrum is taken in $\pu{400 MHz}$ machine. All splitting patterns of remaining resonances are $ddt$ as depicted in fallowing diagrams:





Accordingly, these patterns and chemical shifts well match with N-allyl acetamide (see insert in first diagram).