Alejar equates to many different verbs in English. For your two examples:
Aléjate de ese lugar = **Stay away** from that place.
Entonces ella se alejo lentamente = Then she slowly **walked away**.
Here are a few others:
Al acercar o alejar el mapa, la vista general también cambia = As you pan or **zoom** the map, the overview map also changes.
Quiero alejarme de ti = I want to **get away** from you.
Si el dispositivo no funciona, intente alejarlo de los demás dispositivos semejantes = If the device is not working, try **moving it away** from other similar devices.