Step 1: Understand basicity.
The basicity of an amine is determined by the availability of the lone pair on nitrogen for protonation. Substituents that donate electron density (like methoxy) make the amine more basic, while electron-withdrawing groups (like nitro) decrease basicity.
Step 2: Conclusion.
p-Methoxyaniline, with its electron-donating methoxy group, will be the most basic among the options.
Final Answer:
\[
\boxed{B}
\]