Most tourists visit San Antonio in summer, though it's not the ideal season. The weather is often steamy, and restaurants and attractions tend to be crowded. That said, there are plenty of places to cool off around town, and hotel rates are generally lower (conventioneers come in the fall, winter, and spring) during this time of year. Also consider that some of the most popular outdoor attractions, such as SeaWorld and Six Flags Fiesta Texas, either open only in summer or keep far longer opening hours in summer. Fall and spring are less crowded with tourists, and the weather is much more pleasant. San Antonio is the single most popular destination in the state for Texans, many of whom drive in just for the weekend, so hotels fill up faster and rates may be higher on weekends. The city's business hotels are busy during the week, so consider booking a B&B or hotel that's not business oriented if you'll be staying weekdays.
Climate -- Complain to San Antonians about their city's heat on a sultry summer day and you're likely to be assured that it's far more humid in say, Houston, or anywhere in East Texas. This may be true, but it won't make you feel any less sweaty. From late May through September, expect regular high temperatures and high humidity.
Fall and spring are generally prime times to visit; the days are pleasantly warm and, if you come in late March or early April, the wildflowers in the nearby Hill Country will be in glorious bloom. Temperate weather combined with the lively celebrations surrounding Christmas also make November and December good months to visit. January and February can be a bit raw, relatively speaking -- though, if you're from up north, you probably won't even notice.