for my weekly gig at a Senior Living Facility, I use a roller backpack for my 2" binder and music stand. Sometimes I place my Hawaiian-print, fabric-cased Soprano uke in there as well.
last night at our weekly STRUM (Seattle's Totally-Relaxed Ukulele Musicians) song circle, I simply took my fabric-cased uke and songbook into the Kona Kitchen Restaurant (owner is Yuji Okumoto - bad guy in Karate Kid 2).
I also have a double-racket (tennis) case for ukes (one side) and music stand and songbooks (other side).
If I'm doing a lot of walking I like a backpack, regular or roller. Regular backpack if it's just the uke and songbook and light music stand, or roller backpack if I'm carrying anything heavy like an amp
When I travel (flight to HNL) I place my uke (fabric case or gig bag) into my carryon and have it on the floor under the seat in front of me. Don't worry it's a Soprano and I make sure I don't step on it. I usually get a window seat so there's no passenger traffic to worry about, you know going to the restroom or to walk the aisle
I've been looking at those fiberglass rectangular violin cases for my soprano or concert, music stand, and Nexus 10
keep uke'in',