I wouldn't do an LCD either. It's not worth spending the money on a 24" LCD or something like that, and a 19 or 20" will look very small in the cab. It also won't look very authentic if that is a concern of yours. games do look fine on an LCD though... just not "arcade perfect"
I'd second davieboy's suggestion and see if you can revive the tube unless you know its bad. You can find a 25" chassis fairly easily and inexpensively. Or you can splurge for a new (newish) 25" arcade monitor.
I don't like TVs in cabs, or for playing games in general. That's personal preference really, but I'm not a fan at all.