Tell your hosts part of the truth.--That you are the type of person who needs a lot of alone time, to recharge your psychological batteries. Then tell them to go to the mall without you, as you don't want to spoil their enjoyment of it. Also tell them that you honestly don't mind, as you are not really big into going to bright, noisy, crowded places.
I think I would not tell them about the Asperger's, though. Too many people just don't have a clear understanding of what it is, so "coming out" can cause even more problems. An alternative is to tell them that you are sensitive to bright lights, loud noises, and crowded places.
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If a man does not keep pace with his companions, perhaps it is because he hears a different drummer.
Let him step to the music which he hears, however measured, or far away.--Henry David Thoreau