I've built a couple of BBQ islands in previous houses. The first one was finished with cement board and stucco. The second one I did the stacked stone like yours and it looked much better. I just did string lighting but the LED lighting is better although more work like you say.

It is a lot of work on money to build an island. I'd like to build one for my house now but don't have the time. Probably just go buy one from the grill store.