You got to go to the Aquarium for sure, there are even a few hotels near it and the Lexington. There are rooms right on the beach so you can see the Lexington right out your room door. I cant say much for the beach right there, but Nort Padre isnt far, you can drive down the beach for 2 hours if you want, all the way to South Padre, if you have a 4X4. Find a secluded place for you and your woman to chill and relax or fish. The peer at North Padre is cool to fish off of as well. The Quality Inn has hot tub rooms preaty cheap!
Im getting out of my town tonight too, gonna take my beautiful wife out for a romantic evening in Austin.
Have Fun!! Corpus is great!!!
Edited to say, there is a reastraunt near the Lexington, they have 1LB burgers. Really great atmosphere, and the staff were really nice. I dont remember the name, but im sure you can find it if you ask around down there.