Inspired by beer_good_foamy's drabble on the subject, I offer ten possible reasons why Amy Madison stayed behind in Sunnydale after the Hellmouth collapsed. Some, admittedly, are more believable than others, but I don't think any of them are totally incredible. My own favourite is the last one.
Incidentally, some of these are mutually incompatible - #6 and #7 particularly - so they can't all be the real reason. :)
1. The shock of losing her home, her family and everything she'd ever known drove her insane. Like a rat in a wheel, she just kept going round and round in the same old circles she'd followed before Sunnydale collapsed, unable to even consider changing - until something new shook her out of her depression.
2. She'd tried escaping, just after the Collapse. Her spell backfired badly for some reason, leaving her burned out and helpless for months. Warren had to take care of her, which didn't help matters very much: for food, all he could find were dead bodies. She ate the flesh, he ate the braaaiiinnnsssss.
3. Teleporting somewhere successfully requires a clear mental image of your destination. (Looking at a satellite image is fine, if it's detailed enough). Unfortunately for Amy, every single place she could remember clearly enough was sucked into the Hellmouth and destroyed. She had vague memories of trips to Los Angeles in her childhood, but three years as a rat and one year as a strung-out magic junkie meant that she daren't trust her life to them.
4. It's not possible to teleport through too much solid matter. A few brick walls are fine; sixty feet of rock and compressed rubble is not.
5. The collapse of the Hellmouth created a negative energy vortex that trapped her like a cork in a bottle - just like the Master before her - until an outside force could free her.
6. The collapse of the Hellmouth created a negative energy vortex that sucked in all magical energy in its vicinity, creating a mystical dead zone. That's why the Twilight exploration team couldn't pick up any magical readings - and it's why Amy's magic didn't start working again until she got more than a mile from the Sunnydale Crater. Once she did, she just couldn't stop casting spells again, even in her cell...
7. The activation of Lilah's amulet and the destruction of the Hellmouth created a powerful standing wave of mystical energy in the area. Amy was just bathing in it, soaking up the power, hoping it would make her even stronger than Willow. Only when she'd absorbed all the energy - leaving not even a trace reading for Twilight to pick up - was she ready to announce herself to the outside world again.
8. After seeing what Buffy did to The First's army, Amy was terrified. She wasn't ready to face the world again until she'd honed her skills and built up her power to the maximum. The collapsed Hellmouth was the ideal hiding place, because Buffy and Willow would never want to go near it again, and would never think of looking for her there.
9. She was looking for something buried under the ruins of Sunnydale. Something really powerful; something brought there by one of the countless demons, warlocks, vampires, Mayors, hellgods, minions of The First and other assorted supernatural denizens drawn to the Hellmouth over the centuries. Her search took over a year, but now she's ready...
10. Hiding in the rubble, scampering through hidden underground tunnels. Eating corpses. Planning revenge. Isn't that the perfect life for a rat? Why would Amy ever want to leave?
(Just to be clear: Warren stayed with Amy because he had no choice. All she has to do is say "Let the spell be ended" just once, and he dies a horrible screaming death. Again.)