Your son will send you a letter with the mailing information on it within his first few days...you can also find that information here (sometimes it is posted within days but sometimes weeks).
http://uscgbootcamp.blogspot.com/ Some parents and friends start sending letters on day one, which causes a little extra work for the mail guy/gal as they have to try and figure out who and where your coastie is, while others will wait until they get the official address so that they know the letters will get there. I have sent hundreds of letters to new recruits at Cape May and chose to wait until the address is posted. The new arrivals are so busy those first few days they will not have time or probably even the energy to read mail if they even get to read it...not all CC's allow them to read the mail with out earning it and then most mail reading and letter writing is conducted on Sunday's.
Now I would start writing day one and have those letters ready and on the go button so you can drop them in the mail as soon as that address arrives so your coastie gets to hear his name called out during mail call early and often. The more the better is what they all say after graduating and sharing their boot camp experiences.
Congratulations to your son and your family, I hope you all enjoy your Coast Guard journey!