24/7 Customer Support. When it comes to affordable self storage in Westbury, NY, no one does it better than StorQuest Self Storage. We make it easy for you to save time and money using our servicesCalling all Long Islanders! When it comes to affordable self storage in Westbury, NY, no one does it better than StorQuest Self Storage. We make it easy for you to save time and money using our services. Located next door to the parking lot at Westbury Long Island Train Station (LIRR), our facility is perfect for when you need to drop off a few things before heading into work in the morning. We're also here in the evenings, so you can stop by on your way home too.