If you're using a more popular private park, then yes make a reservations. Texans that time of year love to camp on the weekends, and SA is just south of Hill Country so there is a large population to deal with. Spring break will also be going on that time of year and you will also get competition for sites because of that.
Now if you're planning on a public park with non-reserveable walk up sites, then show up on Monday, Tuesday, or Wednesday and you should be alright for claiming a site for those two weeks. Again spring break can be a game changer in some locations.