castle is only by paid tour, cathedral is free

Entrance to the church (the main part for its OUV) is free

The Big Pit underground tour is free, although you now (2023) can also buy skip-the-line tickets and pre-book.
See museum.wales

pay to see interior of a windmill

Vast majority of the mills are free

Access to the church is actually free, but you will be geared to buy a ticket to the Abbey and pick up an audio guide at the visitor center.
See france-world-heritage.com

The Brihideshwara-tempel in Thanjavur is free (it's an active temple)

Entrance is free of charge, although a donation of $4 for adults $2 for children, and $10 for families is suggested.
See www.cahokiamounds.org

To the church and the stairways

The Iron Bridge at least is free

Seibu Rindon Forest Path is, and I could not find a quote for the trail to Jomon Sugi either

Entrance to the park is free, however there is a parking fee of 600 ISK (5.8 USD/4.9 EUR) for regular passenger vehicles

There's no entrance fee to the cliffs

Some might have an entry fee, but a lot of them are free and there are no obvious major sites among the 727 locations.

You can walk on the aqueduct and along the canal for free.

The sites are free of entrance, but especially at the Kigali Memorial Center you are expected to donate something or buy the audio tour.

Park, museum and Royal buildings are free, observatory isn't

Entry to Mammoth Cave National Park and its surface features is free of charge. There is, however, a charge to tour the cave, stay in campgrounds, or reserve picnic shelters. - NPS *Note: Part of the criteria is based on surface-level features outside the cave itself "Outside the cave, the karst topography is superb, with fascinating landscapes and all of the classic features of a karst drainage system: vast recharge area, complex network of underground conduits, sinkholes, cracks, fissures, and underground rivers and springs." Part of Criterion (viii) for inscription on the world heritage list.

free entrance to the church and park

You have to get a ticket before entering, but the tickets are free

in a city centre but when the chapel inside is open it is free

(last update 2025)

All except for Fort Ancient

The archaeological site is free to enter. The museum & Midas mount require a fee.