The Gravity Mine - a short story by Stephen Baxter
The first time she woke, she was in the ruins of an abandoned gravity mine, built on the ruins of the galaxy from which humans first emerged. The universe would grow far older before she woke again.
Perpetuity Blues - a novelette by Neal Barrett, Jr
Maggie's father disappeared in Strange Circumstances; her mother died watching reruns of Bonanza and Rawhide. And so begins the rocky road to fortune, success and romance, with a little help from a guy who claims he's an alien.
Miguel is a foolish, ill-informed, spoilt youth of the cyberscraper culture. It's Saturday night, and he's alone in the family apartment with the beautiful Maria Del Fuego. But what, exactly, does it take to turn her on?