We had a really great time at Jack & Betsey's in Bywater and we highly recommend this place for different reasons :
1/ the appartment was clean, cute and nicely decorated ;
2/ Bywater is accordiong to us a 'strategic' area as it is quite peaceful but near the Frenchmen street and less than 20 minutes walk from the French Quarter as well, so we could match peace and fun ! ;
3/ New Orleans is big so visiting the city by bikes was just a great fun except that we were not used with Torpedo bikes before so it was kind of wierd at the beginning :) ;
4/ Jack & Betsey are really nice people and gave us lots of good spots to visits (plantation houses, bike rides...), many restaurants and their specialties in the Bywater/Marigny neighboorhoods and aslo in the French Quarter. We had the chance to meet some of their friends who were very pleasant as well...

With no hesitation, we would go back to Jack & Bestey's if we have the opportunity to come back to New Orleans again !