You really can't go wrong with the Fairfield and Courtyard sea world. They are just across 1604 and less than a mile south of Culebra. Probably the closest new rooms to the NSC. And they like shooters.
I used to live in Austin and my parents still are in S.A. I shot the NSCA nationals for a few years and just want to remind you to NEVER leave anything in your vehicle when at the hotel of your choosing. Every year our forums were lit up with gun theft posts all of them from vehicles in the hotel parking lot or parked at a restaraunt somewhere off of that part of 1604. The thieves know good and well the dates for these major tournaments.
That being said, S.A. is a great town with the BEST Tex Mex which I grew up on.
Any chain off of 1604 will welcome you and I have not heard any complaints of "gun unfriendly" management. If you have the money, Hill Country Hyatt is VERY nice but pricey. Your family will love it but your wallet will not as Sea World/Fiesta Texas is near as well as some very good shopping for the wife.
As an aside, Cooper's BBQ is not to be missed. A 30 minute drive or so but well worth it. The best Brisket around bar none. Also don't miss hitting "La Hacienda" for a famous "puffy taco" which S.A. is famous for.
Check with the club, they usually have several "partners" (hotels/motels) that offer a special rate for shooters. You will have to specifically ask the motel for the shooters rate. We used to always stay at the Red Roof on 410 (SeaWorld) and got a great rate. This is one place you can park right in front of your door.
I've stayed at the Holiday Inn Express just off the 410 near Culebra and it's like new -- very quiet, hugh parking lot, 50 yards froma great Texas steak house, near Bill Miller's Bar-B-Q, Denny's for breakfast (the hotel has a pretty decent free breakfast buffet) and I think it was $65 a nite for 2 with 2 queen size beds.
If you haven't been to a shoot in San Antonio let me warm you that the big shoots draw organized gun thieves -- either leave your guns at the club or in your room as they are masters at getting guns out of your car or truck. I was at the World Skeet Shoot one year and was eating at restaurant right off Loop 410 when 2 shooters pulled into the parking lot and parked their SUV right next to the restaurant -- they had their guns in the back in plain view and the SUV was locked. A car pulled -- 3 guys jumped out --- used a crow bar like tool on the back door --- grabbed the guns and them in the trunk of their car and were gone before the owner's could get to the front door.
The police said they were lucky they didn't get outside as the thieves typically have 3 vehicles -- the 1st car is usually an old beater that comes into the parking lot first and takes a position near the exit --- the 2nd car comes in and grabs the guns and scrams ---- the 3rd car has a couple on guys who are heavily armed and ready to shoot if need be. If there is an altercation the 2nd car takes off followed by the 3rd car who clears the parking lot while the 1st waits to see what happens -- it it looks like someone is going to chase after the cars 2 and 3 he will pull into the exit and stall the car "in panic" and quietly abandon the car before the cops arrive.
And they tell you don't wear your ATA, Perazzi, K-80 etc hat around the hotel as it's a sure invitation to have your car broken into a night -- remember there's usually only one or two people on duty in the hotel at night and they're watching TV or doing homework.
The lock-up is more of an Armory. It's staffed by someone all day/night. The guns go into a fix spot. Not sure if they have room for cases also? The area has 3-4 tables inside the door, with some rags and oil, so you can wipe the gun down and check it in. Gun only goes back out if you can provide your tag for the gun (supposedly).
Friend used it last year and was very happy with the service. If you want to check it in/out multiple times a day, it's the same fee per day. If you go eat, check it in, don't worry about it. When you shoot later in the day, you check it out, go shoot, check it back in before leaving the complex. Nothing to worry about when your out/about in SA.
There should be a link at the NSSA/NSCA website to a prior shoot program. All the local hotels have add's in the back of the online program, usually with rates. There's a bunch of new hotels near Sea World, all very clean with decent rates.
When my Granddaughter graduated from boot camp at Lackland AFB we (5 adults, 1 teen) got a suite at a Best-Western. Don't remember the cost but it was very reasonable. Continental breakfast, we didn't use the pool in Dec. It was about 10 min to the AFB, a lot of good places to eat nearby. Larry Evans