Is it legal to keep bees inside of a town's city limits?

Check with your city's ordinances. Might be on their website or you could get copies from city hall as they are public documents.
Depends on your particular city ordinances. You can probably find that on your city's government website.


Answers:
As the others have stated: it depends. If you discover that your town prohibits it, find someone outside town that would let you keep your hive at their place. The 'host family' wouldn't have to lift a finger, they would get pollinators for their garden, and a little honey from time to time if you're feeling generous.