First, know your child. If your son or daughter actively dislikes or is upset by movies, malls or libraries, why force them to come along? Of course, you may need to pop in and out quickly to run an errand, but surely there's no need to involve your child with autism in a two-hour shopping expedition when the outcome is almost certain to be problematic for you, your child, and the people around you.
Second, have a plan. Sometimes a situation, such as a wedding or funeral, requires that you bring your child with autism along even when you know your child will have a tough time. When that's the case, it makes sense to do a little research and planning ahead of time. Your child may do better than expected, but it's useful to have a graceful escape pre-planned just in case.
Third, take risks, but go with the flow. You never really know when a child -- any child -- may outgrow fears or discover a new interest or ability. You may, for example, think your child with autism will hate the art museum, but be amazed and thrilled when he stands in awe in front of a masterpiece. Autism is no reason to avoid the art museum, but it is a good reason to be prepared to leave quickly if things don't work out. Avoid the pitfall of spending too much money on an experience so that you feel extra comfortable walking away when it doesn't work out.