I carry it with me in a ziplock bag and take it everywhere. Even through the scanners at the airport. I explain what it is and show them it they say "ohh, pretty" (even the guys say this) and off I go. I only have the one needle which is on thread so maybe thats why I never had a problem.
When travelling, I take a project box, floss organiser and the cloth. Wrap them up lengthwise in a small quilt or cloth mat(new bought) then bring it along in a large handbag. When sewing, lay the small mat on your lap. Attach your needles in the mat when not using. When closing up, just rewrap everything in the mat and put in handbag.
When I am on the go, I take knitting instead of stitching since theres only a ball of yarn and the needles Im working on stead off a hoop, small needle, many colors, etc. Also, I can knit most basic stuff without even looking at what I am doing, so I dont have to wrry about not having enough light. I cant stitch without my bright bright light!
I do travel with projects. I have a variety of flat zipper bags that can hold everything: the hoop and the fabric, all the threads on bobbins or an organizer in a zip lock bag, a small flat tin with a magnet inside that holds tiny scissors, spare needles, and a needle threader. When I stitch on a larger piece of fabric (think canvas shopper bags) I put the project into a large-ish cosmetic bag and the stuff that goes with it stays in the cosmetic bags inside pockets.
I love my della Q snap pouches- I can keep my yarn in the pouch and take my project out so it doesnt get dirty if it falls to the ground. They come in so many sizes so Im sure you could find one for even your larger projects!