No, you shouldn't have any. As far as I know, the only dealer in HI is on Oahu. If you're based there, you can do service with them. I just had a client buy a QX80 and ship it to the Big Island. Since there are no Infiniti dealers there, we confirmed with the Nissan dealer in Kona that they routinely do warranty service on Infinitis, and just coordinate things through the dealer in Honolulu.
Other good news: If you're there until the lease ends, I'd bet there's a good chance you'll be able to sell the car for a little more than the residual - our cars are expensive in HI, and as I understand it, you don't really get discounts from the dealership since you're a captive audience.
Your out of pocket monthly will change in HI - taxes are likely different than in TX. But just contact Infiniti Finance when you make the move and they should be able to sort it out for you.