Never had a chance to experience The Eagle's Nest. If it was better than NikZ I'm extra regretful.

I mentioned this thread to my wife and she not only provided me with the name of the BBQ Shack (Tom's BBQ) but also provided three more locations that immediately came to her mind:

Triples (for the Monte Cristo Sandwich) (I never made it to Triples).
Bennigan's (ditto on the Monte Cristo) (had one here, to me these are far, far too "cloyingly battered/sweet")
Molly Murphy's ("for a birthday") (Never ate here but did get to see just how greasy and dirty a kitchen could get, just before they closed their doors).

Ditto on Han's BBQ.
(and I never got to try Nicolosi's, but hear that it was pretty darn good)