I usually have it in a backpack for breaks at work, and a smaller shoulder bag (my wife calls it my “Tactical Man Purse”) for when I’m out and about on my days off. It lives in a Smatree P100, also encased in a Cosmos Black Hardcase.
I don’t know how hot it gets in your part of the world, but leaving your Vita in a car for any length of time when the weather’s hot can be bad for it over time. I know from experience that it loosens the adhesive on any tempered glass screen protector you might have on it — gave mine a big bubble and had to be replaced — and high heat over time can degrade or damage the battery.