The cat bag is a cute idea (or maybe I just like it because one of the cats looks like mine). I don't think I would use it though, as it really does not afford a cat any protection from another animal (at a vet office or campsite). In fact it looks like it would keep the cat from escaping if it were in harm's way.
The soft sided carrier looks better from a safety point of view. My cat just has to "deal with it" when she's in her dreaded hard-shell travel case because I know it's her safest alternative.
We also havae one of these
PetGear strollers.so she can go on walks and to farmer's market and such with us. Not sure it would fit your needs (and space contstraints) though.
We've stayed at Red Roof Inns when necessary and no mention was made of a cage requirement. At HomeWood Suites and Residence Inn, however, they required my cat to be in a cage any time we left the room. (Outrageous pet fees on those last two, by the way.)
(EDIT: NOT AN ADVERT)