Lots of good recommendations already in the thread. Been living here 4 years and here is what we like for date night spots.
Yardarm - semi casual, great seafood, lots of charm in the old building if you are into that sort of thing.
Fork and Vine - new place, still working out the kinks but food was good
Blue Clove - casual, great seafood
Dokyo Sushi - "trendy" for Corpus Christi, but I like the sushi and the cocktails are good
Vietnam - probably some of the better food in town overall, the chateaubriand is great (I think they may only have it on weekends?)
The one place I have started to avoid is Republic. When we first moved here, I enjoyed it, but the last 2 times I have been the service and drinks were great, but the food was not. It wasn't terrible, but not for high end steak house prices. Just my opinion.