Here are things that have been given as gifts. They are listed in no particular order. Feel free to add other ideas.
Gifts that can be taken back to RTC:
Personalized study Bible or Sailor's Bible (This can be taken back to RTC, but your Sailor may ask you to send it later depending on space.)
Religious medallion or cross to go behind his/her ID tags (dog tags) or on a neck chain or key chain. (They seldom wear their dog tags after PIR and "A" School though due to safety concerns, but must be able to produce them during inspection if asked.) If worn with the dog tags, it must be silver in color and must be smaller than the dog tag. If worn on a neck chain or key chain, it can be any color. (If on the dog tags, this can be taken back to RTC.)
Gift cards to the NEX or national restaurants or Walmart or Mastercard or Visa gift cards that can be used anywhere. (You can go to https://www.shopmyexchange.com/scs to get a NEX gift card if you have a DOD number and register with the site.)
Phone card (Remember that your Sailor will have access to his/her cell phone after checking in at "A" School or the training location or after arriving at the air port, but your Sailor may need a phone card to call you from the air port and may need one later.)
Wallet (There are some with Navy emblems or the blue/gray digi print or the green camo print.)
Money Clip (Some have had it engraved with the Sailor's name and sometimes the date of PIR.)
Watch (black or silver in color) They can have a gold watch, but most choose not to get gold since the insignia for Sailors through E-6 is silver and the insignia for chiefs (E-7 and above) and officers is gold. Some ratings may require a particular kind of watch. (The Casio G-SHOCK watches are very popular with some new Sailors.) Sailors can wear a watch of any color as long as it presents a professional appearance, which is why most prefer black or silver, but navy blue colored watches are also popular and those with brown wristbands are acceptable. There are nice Casio watches that cost $10 to $25 that some Sailors get and they don't have to be concerned about them being broken or stolen. Get a pocket watch for those who cannot wear jewelry on the job. If you get an expensive watch, then do engrave it--my Sailor recommends including XXX-XX-(last four of SS #) so that there is no doubt as to the owner. Apple watches are not authorized for wear in the Navy. (See https://federalnewsnetwork.com/defense/2015/10/navy-oks-wearable-fi....)
Earrings (silver 4mm - 6mm ball, plain with shiny or brushed matte finish, screw on or with posts) (Females can wear these back to RTC.)
Ring (Navy rings can be ordered at the NEX or from Jostens.) (Some ratings cannot wear rings. Sailors can wear only one ring on each hand.)
(http://www.public.navy.mil/bupers-npc/support/uniforms/uniformregulations/chapter2/pages/2201personalappearance.aspx has the jewelry standards for the Navy.)
Challenge coin for RTC (available at a MWR booth in the Drill Hall, in RTC Recreation Center in Bldg 1326, at the NEX and online at https://picclick.com/US-Navy-Recruit-Training-Command-Great-Lakes-Challenge-161125990453.html and other places such as pirgifts) and/or the Ship the recruit is on (Craig designed the ones that are available on eBay through pirgifts and there are different ones that are available at the MWR booth). My Sailor told me not to get him a Challenge Coin because he wanted to keep that for those who give it to him within the service and not me--he only has one from RTC because Craig sent him the one for his ship since only award winners receive coins while at RTC. You have to decide what is right for you and your Sailor. One mom bought a few for her Sailor to give to his closest shipmates. (See more about Challenge Coins in What does ??? mean? (A Guide to Navy Abbreviations and Terminology).)
Recruit Care Package This is good if you cannot attend PIR. They often include the RTC Challenge Coin.
Gifts that will have to wait until your Sailor has checked in at "A" School or the training location or is at the airport:
iPod (preloaded with some favorite music)
Portable battery charger to charge cell phones and other electronic devices
Mobile Hotspot (Although most "A" Schools do have a location for free WiFi, it may not be the best and may not be in a convenient place for your Sailor.)
Pocket knife or compact multi-tool (blade of 3 1/2" or less, no fixed blade or tactical knives) *Some commands may have regulations that are more strict than this.
Iron and small ironing board
MP3 players and iTunes gift card
Mini sound system
Personal DVD player and subscription for DVD's
Soft sided case for DVD's (You can include a few favorite movies.)
Quilt or blanket made especially for the Sailor
Sheet set (Twin size) (Some like those at http://www.navysheets.com/.)
Photo album or digital photo frame with family pictures
Security locks for laptops and other electronics
Travel alarm clock
Skincare items (sunscreen, hand lotion, and/or lip balm) with sunblock, especially for those in aviation
A nice razor and shaving cream kit
Conservative sunglasses, especially for those in aviation. Nothing "faddish." Matte metal or black are the best choices.
NavyRackPack (If your Sailor has orders to a particular ship/sub before the end of BC, which happens for those in the PACT program, this is a great gift. Go to http://www.navyrackpacks.com/. Email Pat and she will let you know which one to order. Keep this one in mind if your Sailor is ever on a ship/sub. My Sailor said his was "awesome" when he was on a carrier.)
Kindle or other electronic book reader and gift card for electronic books.
Small flashlight. If they are headed to a ship, a mini maglight with the red lens option.
Socks and underwear
Nice white undershirts (Look for Dryfit material)
Fun playing cards
Camelbak water bottle
Good pair of running shoes (Those issued at BC may be worn out even if they still look good and could cause injuries.)
A nice journal
A small notebook with moleskin cover
A nice pen set (a pen that will hold up)
Shirt Stays to help keep the uniform shirt tucked in
Eisenhower Jacket (a plain black jacket)
If you get an expensive item, then do engrave it--my Sailor recommends including XXX-XX-(last four of SS #) so that there is no doubt as to the owner.
Gifts to be enjoyed at the hotel or away from RTC:
Favorite homemade food and/or purchased junk food
Time alone to shower at the hotel (have favorite underwear available and comfy clothes available to change into; remember your Sailor cannot leave the hotel room in civilian clothes)
Time with that special someone
Time to relax (computer time and/or movie, junk food, favorite soda....)
Manicure and/or pedicure
The most important gift you can give your new Sailor is your love and support. Hugs are precious for everyone.
The above information is provided by lemonelephant, the mom of a retired Sailor.