What are my options for storing NXT outside of a centralized exchange?
In the blockchain through the client.
If you don't want to download the blockchain, try mynxt.info or mofowallet.com. mynxt.info also have andoid and iOS apps.
I'm very careful about what I install on my computer. Can I install NRS in a sandbox somehow? I suppose I could run it as a very unprivileged user. I use Linux BTW.
I think a web wallet is too risky.
Would Jay be a good choice?
mynxt.info online wallet isn't any different to using a centralized exchange, except it uses the blockchain linked to an account you create using a username and password.
I've heard some people use virtualbox? Or even boot Linux from a CD everytime. I don't know Linux well.
Beyond that, you would need to create a thread in nxtofrum or use the main thread where more people than me will see it
Nxt 'Official' Thread: https://bitcointalk.org/index.php?topic=587007.0