In this case OP doesn't even come off looking that great in her own post - she seems a bit like a moody teenager.

OP, when someone takes you on a trip with them, you generally try to seem like you want to spend time with them. Even if you refuse an invitation somewhere, it's helpful to pad it with another time to see them. Something like "I think I'll sit out the exhibit, but lets get together for lunch after." Refusals also go down better if you have an activity you'd rather do instead. "Art isn't really my thing, I thought I might go do some shopping while you're at the exhibit."

If you are refusing an invitation in order to sit at home with your tablet (without giving an illness/feeling tired excuse) it looks bad. It looks like you don't want to spend time with your hosts, and that you think that the location they took you too is so boring that staying in on your tablet is the most interesting thing you could think to do.

Apologize for being out of sorts, and say you were just feeling a little tired from being in the sun for a few days and wanted to rest. Then suggest another activity for tomorrow.