Kate, how long will you be
plant-sitting? If your landlady is going to be gone for less than 3 or 4 weeks, she may as well have left the Spider at her place (unless her house will be getting too cold while she's away).
Spider
plants like their soil to get very dry between waterings, & if you water them too much the leaves will start turning brown. I water mine about every 3 weeks in the wintertime, & a little more often during the summer when the humidity is lower. If your heat source dries the air out a lot (like wood heat, for example) you might want to check it for moisture by sticking your finger down into the soil, & water it more often if you don't feel any dampness.
Spiders don't do well in low light, but they won't tolerate direct sunlight. Bright, reflected light is best.
When I was away for a few weeks a couple years ago, my husband watered my Spider
plants & Aloe Vera every 2 or 3 days, & drowned everything before I got back! (He thought he was doing the right thing, but I'd never thought to mention to him that those
plants thrive on neglect!) I had to repot the Spider right away to get it out of the wet dirt, & it survived but it took a couple months before it perked back up! The Aloe was toast.
Good luck!