I've never lived there, but I visit it several times a year either directly or en route to other points of interest on the Texas coast. Corpus seems to have the typical sprawl of any mid-size Texas city, but certainly nothing like the larger cities of San Antonio, Houston or Dallas/Fort Worth. I'd go with the 400,000 population number, if one assumes that accounts for not just Corpus Christi's city limits but the growth on the outskirts of the city as well.
Corpus Christi is more bicycle-friendly than my hometown San Antonio, but that's not saying much. It's
not as bike-friendly as, say, Austin. Most of the folks I see biking are not serious riders, but there are
some cycling clubs that serve the area. Areas near the university (Texas A&M - Corpus Christi) are probably the most bike-friendly, and there are some nice city/county parks for walking and wildlife viewing/birding.
The attitude of the town? It's a coastal town... even in winter, it feels like a coastal town in every way -- tourists mixed with locals, fishermen, boaters, birdwatchers, windsurfers, beach bums, families. There are some nice restaurants and hotels, but by and large it's a laid back, "come as you are place", unless you're walking into one of the high-rise businesses or showing up for work at one of the petro-chemical plants.
What sets it apart? You'd have to ask a local to answer that. The appeal for someone from out of town is Corpus Christi serves as convenient access to a beach vacation year-round. It's a birdwatcher's paradise, as are many of the towns along the Texas coast, with many migratory and native bird species observed. It's got beach resorts nearby (Port Aransas, Padre Island, etc.) and you've listed the various popular tourist attractions -- the aquarium's terrific (better than anything we have in San Antonio); the U.S.S. Lexington museum is educational and a worthwhile visit; there are several art musems and a natural history museum; and so forth.
Hope this helps.
I'll probably never live in Corpus Christi, but that's only because I can't imagine my home and automobiles getting soaked in the salty sea breeze, and I'm not keen on hurricanes. I do love
Padre Island National Seashore with its white sand dunes and 4x4-driveable beach... although the water can look uninviting to folks who've seen Florida or California waters.