The South Carolina Aquarium doesn't allow outside food. If you go around lunchtime, there are plenty of places to sit and eat your lunch outside prior to entering.
The aquarium is always open, except during national holidays. In the spring and fall, visiting during the week is best.
The best time to visit Charleston is during the spring (March to April) or in the fall (October to November). The crowds start coming during June and stay until October (since this is high wedding season). It can also get incredibly hot and humid come July and August.
At the aquarium, toddlers (age 2 and under) can visit for free.