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This inflatable carseat rolls up and stows in a neat 7" tall by 5" diameter package (or you can lay it flat at the top of your checked bag). It's not comfortable enough for long drives, or as a daily use carseat, but it's great if you'll be hopping in and out of taxicabs or need a booster to get you from the airport to your destination. When we're not traveling, I keep mine in my trunk for unexpected carpool situations.
We prefer not to lug our carseats through the airport. Instead, we use a lightweight CARES safety restraint when we fly. It is FAA approved, easy to set up, weighs only a pound, and has made getting through the airport much easier than it was in the days when we brought a car seat. Best of all, we know that E is seated safely. He likes having a little more space than his car seat would allow, and sleeps well in it. It's perfect for trips where we travel exclusively by plane, train and subway or can rent or borrow a carseat at our destination.
This is the replacement for the popular Sunshine Kids Radian 80 Car Seat that I bought for my own kids. It bills itself as the only carseat you will ever need. Because it works from birth until 80 pounds with a 5 point harness, and to 120 pounds as a booster, that is likely to be true. The seat folds, meaning that it is less likely to be damaged in transit than a traditional seat, and that it will fit more securely on a luggage cart. Sunshine Kids manufactures a Travel Bag for checking the seat, and a Car Seat Carry Strap that lets you carry the seat over your shoulder (or with two straps, on your back).
Don't expect to carry it easily through the airport to your plane, though, the seat weighs a hefty 24 pounds, meaning that it might be best to check it curbside and use a CARES harness onboard.
This car seat alternative is small enough to stow in a daypack or check in your suitcase. To "install" it, your child puts on a vest, and you connect the car's seat belt through the vest. This works great if you have to jump in and out of taxis or will take a van ride from the airport to your destination. The vest is less comfortable for long trips in hot weather, and you should be aware that kids will be seated on the car's seat meaning that they'll be less able to see out the window. The RideSafer Travel vest is available in two sizes Small 3 - 6 years or 35 - 60 lbs. and Large 5 - 9 years or 50 - 80 lbs
The Sit 'n' Stroll is essentially a car seat with a built in handle and wheels so that you can also use it as a stroller. It is approved for use on airplanes, and on some planes, you'll be able to wheel it right down the aisle. While we don't use the Sit'n'Stroll ourselves (we just avoid needing a car seat altogether), I do think it is a great product for trips where you will be in and out of a taxi a lot at your destination. It's a bit less great if you will have a rental car at your destination because you need to re-install the seat each time you put the child in it, but still workable. The stroller feature is good for airports and city streets, but not designed for rougher terrain. The Sit 'n' Stroll fits newborns (and can be installed rear facing) up to 40 pounds.