What is the difference between "check something" and "check on something"

Solution 1:

Check means to examine (something) in order to determine its accuracy, quality, or condition. Check on is a phrasal verb that means verify, ascertain, or monitor the state or condition of.

It's a subtle difference between the two, and, in the example you gave, I think either could be applied.

If you asked me which one was more correct, I think I'd vote for check, rather than check on, but that was only after consulting a dictionary. Most tourist officers aren't that careful with their words before checking up on the hours of a village shop.

Oh, check up on means investigate in order to establish the truth about or accuracy of, which is, I suppose, another way of saying (nearly) the same thing.

_{Ref: these definitions were taken from NOAD}

Solution 2:

Check on is used to refer to verifying the legitimacy or the condition of someone or something, according to Free Dictionary.

I reckon, check is better suited in your example.