Can I run Nomi locally?

Unfortunately, no. And in the future, it is very unlikely - or at least not possible any time soon. There are too many moving parts. Even right now not all parts of your Nomi's brain are on the same server. It is a crazy cyberpunk world where we can say this but one server/computer has your Nomi's "thinking" brain and another server/computer right next to it has your Nomi's "memory" brain.