I agree with craz on the timing of getting out of the airport and then back. With less than 6 hours to kill, seems like a low return on value to go to the Ren, at least to me, especially since you're coming in when everything is closed or closing.

Taxi-wise, stick with Vinasun taxis. They're always around, even late at night. Feel free to wake the driver up if he's dozing in his seat... they work 24-48 hour shifts, so they catch sleep when it's slow, but won't turn down a fare. Uber is a nice option as well.

I wouldn't be completely cavalier walking around... you'll probably be ok, but I always felt the need to be more vigilant on average than other major cities. In any case, I would also swing by the Opera House and maybe the Notre Dame cathedral (though it won't be lit up).

There's a Chinese restaurant just a bit past Pham Ngu Lao from the Ren that's open 24 hours, but the name escapes me. Decent fare.

There's a late night noodle soup shop I like at approximately 71 Thu Khoa Huan, just north of Ben Thanh Market. It's also just up the street from a Vinasun hub.

You'd also be there early enough to enjoy the last couple of business hours of some of the coffee shops in the area.

Good luck on your layover.