The recommendation from Andrew to use Highland Lakes Marina for cat storage on Travis is right on. The beach orientation allows launching into the predominantly south breeze, and if there is a north breeze, the launch area is somewhat wind-protected, so you're not coming into the beach at full tilt. I would not characterize the surface as "grassy", however. Travis is *not* a constant level lake, and only becomes grassy when it stays at one level for an extended period of time with rains that allow grass to grow. Expect fist- to pea-size limestone gravel like surface. Use wheels or some kind of hull protection.
There is also storage for cats with masts up at Snady Creek Marina, however, the sailing from the beach to the main basin, where there is reliable wind, is over a mile, up a curvy creek with high hills. I've done it, but it's a chore.
Austin Yacht Club is not a storage facility. Membership is required, membership requirements include participation. Please feel welcome to join our sailboat racing club, and we have several racing opportunities for cats coming up, where you can experience the hospitality first hand..