Hey there, zygisg! Congrats on the move to Nag's Head -- it's absolutely beautiful there. You can find the full list here: T-Mobile network. I'm happy to take a closer look at the specific area where you'll be located as well, if you'd like! The Outer Banks coverage varies in different locations -- will you be in Nag's Head proper, or closer to Hatteras?
Your phone should be able to work on 2g,HSPA+, and LTE in some locations. Your missing bands 4 and 12 which is a big chunk of T-mobiles coverage. Hope that helps.