Def second BAT in the Highlands - food cant be beat. But the atmosphere is far from "fancy" and I don't think they would accommodate a party. I'd try Citrico's in Bradley Beach nice intimate atmosphere above average Italian food and theyare VERY accommodating and would probably close down for a party. or Angelicas in Sea Bright Is also very good but not sure about a party there. Tulipano's in Belmar is another option. They def do private parties but their service is very hit or miss.
I think this is all the nicer BYOs in the area...is anyone familiar with any of these places?