Why is it that the PH of my tap water goes up a little after the water sits out for a day?

How much is a little? Could be due to evaporation although I'm not sure it would be detectable after only one day. It could also be due to any substrate or rocks you have in the tank. Or were you talking about keeping water in a bucket for a day?

Yes I just put some out in a cup for a day. I was complaining the low PH of my tap water and someone asked me how the PH was after some sitting out for 12 hours? so I tried it with RO water, too. I think that's very interesting that the Ph would go up with it sitting out.

If you are testing with strips the accuracy would be off. Also you may see a slight pH difference between cold and warm water because temperature effects the concentration of hydrogen ions, which is what can effects pH values.