Corpus Christi is just another city in Texas.Don't expect much. But there are two places "padre island national seashore" & "south padre island".  Padre island national seashore is about 45 minutes from Corpus Christi (but a very weak cellphone signal place). It costs about 10 dollars to enter. I have not been to South Padre Island (which seems to be a fun beach) but Padre Island is "very beautiful" and "almost virgin" beaches. If you have got 4WD you can drive on the shore & go to South Padre Island (what an adventure). (Don't try with your car), you can play in sand dunes too. Evening is the best time to be there. NO Visa issue at all. If you go to South Padre Isalnd on right time there will be another kind of fun as mentioned by others.