New Orleans 2 Nights in June

My family of five is visiting New Orleans in June. It’ll be our first time so we were looking for a semi-authentic feeling ‘New Orleans experience’ hotel with a pool in the French Quarter that won’t cost more than $200 a night. For any locals or past visitors - is there a hotel with a pool that has the New Orleans vibe (balcony along the street, etc) that you could recommend? There seem to be a lot of good options but I’m not familiar at all with the different parts of the Quarter and what might be a better general location. Thank you!