Replying to Small travel camera advice?

My girlfriend is going to be spending a semester in Vienna (and travelling around Europe), and asked me for advice on a camera. I thought a used sony rx100 would be perfect, especially because keh has them under $300. Came here to see if anyone had any other suggestions. Here are the requirements.

Small: thinking deck of cards sized, something for a coat pocket or purse. Not a dslr, not a "bridge" super zoom

Price: the lower the better

Low light: she will be visiting lots of old cathedrals etc., so it needs to be able to get decent pictures with no flash.

Lens: fast, wide, has to zoom. 28-70+ would be good. Wide enough for group shots/indoor etc., enough reach for things you can't walk up and touch (altar, stained glass window, band on stage from crowd etc.), but nothing crazy.

One of the most important features is having a decent automatic mode. She will leave it in this at least 75% (probably 100%) of the time starting out. I've told her some of the basics and she has used my dslrs, but I always set the exposure for her. Along with that, an easy to use "no flash" mode is a must. Concerts/churches etc. don't like flashes, and it would be nice fire her to be able to get non blurry shots without getting kicked out.

Video isn't super important.

Battery life: should last for at least a day of casual use, a weekend would be better. If extra batteries are cheap/easy to find, that would work too.

Image quality: should look good, most will go to facebook/shared with family. Some might get printed, especially if she gets some shots she likes, but I think they will be primarily viewed on the computer.

I'm on mobile now, but I think that is everything.