I rent a house in North Carolina, and accidentally left a2'x4' patch of the lawn covered for too long, killing off the grass beneath. My landlady has asked me to reseed the lawn as soon as possible. I'm unsure as to what type of grass to buy, or how to start the seeds at this time of year.

The patch itself gets full sun, but is just outside the drip line of a black walnut, which (I believe) has killed off nearly all the grass in the shaded area. The lawn overall is very patchy and not well tended - lots of other little plants growing in with the grass, and lots of bare patches all around. Water is also an issue, as this area is in a state of moderate drought and under some fairly stringent watering restrictions.

Ideally, and I know this is a tall order, I'd love to put something in that can fill up the patch as well as grow closer to the walnut, wouldn't require a ton of water, and wouldn't cost too much. If that's completely impossible, then something relatively inexpensive that will fill in the bare patch would be fine. If THAT is also difficult, what should I do with the bare patch until a better grass-planting season comes around?

Thanks so much for your help!