The Beast from 20,000 Fathoms
I just finished watching The Beast from 20,000 Fathoms, one of the first ever Creature Features. Long story short, a nuclear test in the Arctic (what?!) awakens a hibernating dinosaur, the remains of which have only ever been found in the Hudson Canyon. It makes its way south destroying several boats and a lighthouse (stealing straight from Ray Bradbury's The Fog Horn, one of my favorite short stories as a kid and still worth reading) before rampaging through New York City (where obviously it originally lived).
Stupid cops. It doesn't count as post-apocalyptica but I still love it. Ray Harryhausen (of course) did the effects. You can watch the entire thing here if you must but it wasn't actually that good.