**Patra-Bannk[/B in Tony Rothman’s the World is Round. I don’t want to explain it, because that would ruin the story. suffice it to say that the world seems unreasonably big for its density
Rocheworld, the setting for several of Robert L. Forward’s novels. It consists of two close-together worlds filling the Roche limit with weird and interesting effects (including an intra-planet waterfall
Forward’s Dragon’s egg – a neutron star with intelligent life on it, the setting for two of his books.
I see that I am one of the few who took the OP’s request as referring to physically interesting worlds. There are plenty of societally interesting ones.
George Gamow’s Mr. Thompkins in Wonderland has several versions of Earth that demonstrate relativity and quantum effects as if they existed in the real world. There’s the view of a quantum pool table (the balls stretch out into multiple probabilities as they are struck). The most memorable is a world where the speed of light is 10 mph: from the street, people become narrow as they ride a bicycle, while on the bicycle the telephone poles move together. There’s also the old woman who comes up to a young man coming off a train and saying, “Grandfather!.”
John E. Stith also played with the speed of light on Redshift Rendezvous, set on a spaceship where different levels have different speeds of light.
There’s also David I. Masson’s short story “Traveller’s Rest,” which has a world where time moves faster the nearer you get to the poles.
The Earth and solar system of the Clockwork Trilogy, in which the solar system is a vast orrery. The Earth and all the planets move about the central lamp of the Sun guided not by gravity but by planetary-scale gears and wheels and springs.