The LAX Hilton is pretty good. I've only stayed there once but I've been to a lot of events there (without booking a room). The restaurant is very expensive for what you get but the food is OK. The cafe/bistro is quite good, except for the employee who always makes fun of my British accent (despite having some sort of accent, possibly Caribbean, himself!). What else...hmm...oh, avoid Carl's Jr. down the street. IMHO it's the worst out of all the fast food chains (even worse than McFatty's). There are shuttles that go to and from the Hilton from the airport so you won't have any worries there. There are car rental places within walking distance of the Hilton (though you'll probably want a shuttle or taxi if you are carrying lots of luggage).
I've never been to Hawaii but would also be surprised if you had to go through immigration at LAX. Since HI is a US state, that wouldn't make much sense to me since it's really an internal flight.