I went to Carlsbad Caverns about a month ago. Assuming you're just going to do the main cavern tour, there is artificial lighting everywhere, and paved paths with handrails.
Their website says that they don't allow tripods, but they actually do. Unfortunately, I did not know this until after I was inside and saw a dude carrying a big tripod around. I had my mini-tripod with me, which I could sit down on benches or other places where there was a convenient flat spot at a decent height for getting a shot, but it definitely wasn't ideal. Mostly, I used my tripod as a chestpod, which worked some of the time. Usually I shot 3-shot bursts, so 1 of the 3 would end up being reasonably sharp.
They do allow lights of all kinds, including camera flashes. So no problem there. But there are some features that are very large and far away, that a P&S flash might not be able to reach.
I will definitely take my full-sized tripod next time, but it would still be less than ideal, especially on a crowded day. The walking path is pretty much the width of a standard sidewalk for the whole thing, and you'll definitely get scolded by the Rangers if you block the path. I was actually thinking that the ideal "tripod" for this location would be some kind of clamp that you could use to grip the ubiquitous hand rails (which all seemed to be metal poles, roughly 2" in diameter). Something like this:
http://www.amazon.com/Electric-Avenu.../dp/B001CWF8ES
Here are some photos that I got there. I used my Canon 5D and 24-105 f/4L IS. The ISO was 1600, aperture f/4, shutter speed from 1/8 to 1/2 seconds (most at 0.3 seconds). I wish I had brought my large tripod, or that I had a fast wide-angle prime such as a 28mm f/1.8. None of these are particularly good; they are all pretty blurry when you view at 100%, but at web sizes they look pretty nice.
A few more at the link:
http://imgur.com/a/lnQ1a