Carrying your instrument on board is always the safest choice. For small instruments like ukulele, this should be easy, no questions asked. But even for guitars and other larger instruments, the FAA has regulations guaranteeing that musical instruments can be brought on board as a personal item as long as they can fit in overhead compartments or under your seat like other luggage. You can find it by searching "FAA musical instruments." I recommend taking a screenshot of this policy as well as your airline's musical instrument policy to show to any airline staff who might have questions.
If you want to use a gig bag to carry your instrument on, I'd recommend an impact-resistant one like those by Reunion Blues
or the Taylor Aero Case
. They're not cheap, but cheaper than a new guitar. Best practice for travel is always to use a hard case when possible, especially for larger instruments that may have to end up in the cargo hold. TSA-ready cases like those made by SKB
or Gator's GTSA series
have TSA-approved locks, so they can be securely checked in without the worry of TSA destroying your lock if they decide to inspect your instrument. You can also use TSA-approved luggage straps to retrofit/secure standard hard cases for checked baggage.
If you do decide to check your instrument as luggage, or an airline employee says there is no room for your instruments, ask to "gate-check" the instrument. This means that you will bring it all the way to the plane before it is loaded in the cargo hold, so you'll be in control of it for more time and it will be last loaded/first unloaded. The flight attendants may have room on board to store it as well - they often have a closet available for storing personal items like strollers.
Ben, Guitar Specialist