I've had lychee (not really fresh, but either in jellies or cut up in bubble teas) and loved it, starfruit was good, and I LOVE pomegranate. For the latter, I don't know if I've ever learned a "right way" to eat it, but generally after forcing my way into the rind initially, I just kept tearing through it and picking the seeds out by hand.

*drools* Now I want one.