12 hours in Krakow, early morning on National Day

score:5

I once asked a similar question and it was closed as off-topic, but I could recommend:

Walk around the ring park (Planty). Somewhat like Vienna, this park was created by the demolition of the old city walls. As you say, it will be dark, but there are interesting monuments throughout, including some remaining old gates, and a good way to see some of the old city on this 4 km loop. You can walk around (but probably not into) the Wawel. There are views of the river and statues of a dragon and a dog on this side. For a longer walk, you could continue along the river and see the site of Skałka, which has historic and religious significance.
Attend a Catholic mass, if this interests you, in one of the historic churches that are likely to have a morning mass. On the main square, St. Mary's Basilica is perhaps the best known, but the nearby Basilica of St. Francis of Assisi is within walking distance and beautiful in a more modern style of decoration. Mass times are usually posted online.
Try to arrange a private tour or class; individuals who offer these may be able to accommodate unusual holiday hours and may have special access to some sites. You can find someone to drive you around Nowa Huta (the Communist planned suburb) in a Trabant (a loud little East German car) or teach you local cooking.

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