There are a total of 17 audio diaries in Episode 1 of BioShock Infinite: Burial at Sea. For each diary I tried to pick out the best starting location that stands out or is easy to remember. Remember to lookout for lock picks, because they are required in order to access some diaries. There is the option to reload a chapter if you miss a diary.
I've included timestamps for each audio diary in the description section of my video. I hope you find my video helpful!