We recommend to book your stay in the following neighborhoods: Bocagrande, El Laguito, Old Town a.k.a The Walled City, Getsemaní, Manga, Crespo, o El Cabrero.
Both Airbnb and hotels are a great choice.
Flight
Rafael Nunez International Airport (CTG)
The airport is conveniently located within the city and only a 20-30 minutes taxi ride from Downtown and Bocagrande.