I thought the ending was fitting enough. There weren't too many other ways they could have gone with it that wouldn't have made it a hacky typical Hollywood ending. As far as whether or not a Nuke was used, I was under the impression that they used a daisy cutter type bomb. In otherwords, a bomb with incredible explosive/destructive power, without the radiation associated with nuclear/atomic bombs.
MANY SPOILERS AHEAD!
My biggest gripes with the whole film came in the last five minutes of it though. First off, you have Hud dropping the camera, going back for it, and realizing he's underneath the monster. How exactly does a giant monster sneak up on you in the middle of Central Park? In the beginning of the movie the monster's footfalls were causing tremors, this time I guess he tip-toed up to Rob, Beth, and Hud.
Second gripe. Why did the monster I just mentioned who snuck up on Hud look so damn small compared to how he looked in the rest of the film? If it was the same size as previously shown it wouldn't even notice Hud. And even if it did, and ate him, there would be nothing left of that camera or Hud's corpse to come falling back to earth. Unless there's just more than one monster, which is quite possible, this scene wasn't congruous to the rest of the movie.