The Texas Surf Museum is a fairly small one, located directly downtown. It houses displays about surfing with an emphasis on surfing the Gulf Coast. Check out the neat mural and the board-shaping garage. Also has memorabilia about Hollywood and Surfing. Open daily. Admission is free.
I do enjoy looking at art; but am much more interested in a science and/or history museum. And the Corpus Christi Museum of Science and History is a good one. Learn about a 1554 Spanish shipwreck that occurred near here; see an authentic carved dome ceiling from 16th Century Castille, Spain; Smithsonian exhibits, and a variety of other rotating displays. You can also tour replicas of the ships Santa Maria and Pinta used by Columbus for his explorations of the "New World". Hours are 10 AM to 5 PM Tuesday through Saturday and 12 PM to 5 PM on Sunday. Admission is Adults: $12.50; Senior Citizens: $10.00; Military (active with I.D.): $9.00; College Students: $9.00; Children (5-12): $6.00; Children under 5: Free.
The Art Museum of South Texas houses impressive permanent and rotating exhibits of historical paintings, photographs, handcrafted items and murals, all in an interesting setting provided by a building designed by renowned architect Philip Johnson and a location right on Corpus Christi Bay. There are a few sculptures outside too, ranging from a nice one of a bucking bull and one of those that makes me scratch my head and wonder what it is. Hours are 10 AM to 5 PM Tuesday through Saturday and 1 PM to 5 PM on Sunday. Admission is $8 for adults, $6 for seniors and active military, and $4 for students 13 and up.
The Art Center of Corpus Christi houses a large gallery displaying the art of local amateur and professional artists along with working studios of four artists so you can see the creative process in progress. The center is housed in a 14,400 square foot building built in 1942 as a USO Club. To me, the building was as impressive as the art. The center is rented for weddings, receptions, luncheons and similar occasions. Hours are 10 AM to 4 PM Tuesday through Sunday. Admission is free.
There is a nice water garden with a shaded walkway located between the Art Museum of South Texas and the Corpus Christi Museum of Science and History.
The Nueces County Courthouse, in keeping with a large modern city, is large and modern looking. Like most of Corpus Christi though, it has remained kinda pretty.
Corpus Christi has great beaches downtown, it's a great waterfront with paths for jogging and rollerblading.