From my answer to the related question: What are the Wonders and the Wonders Made by Man? we see what the Wonders and Wonders Made by Man are/possibly are. From the quotes on the Q/A we can clearly see Tyrion is highly intrigued by them and would like to see them all.
"A scribe, long dead," said Haldon. "He spent his life traveling the world and writing about the lands he visited in two books he called Wonders and Wonders Made by Man."
"An uncle of mine gave them to me when I was just a boy," said Tyrion. "I read them until they fell to pieces."
"The gods made seven wonders, and mortal man made nine," quoted the Halfmaester. "Rather impious of mortal man to do the gods two better, but there you are. The stone roads of Valyria were one of Longstrider's nine. The fifth, I believe."
"The fourth," said Tyrion, who had committed all sixteen of the wonders to memory as a boy. His uncle Gerion liked to set him on the table during feasts and make him recite them. I liked that well enough, didn't I? Standing there amongst the trenchers with every eye upon me, proving what a clever little imp I was. For years afterward, he had cherished a dream that one day he would travel the world and see Longstrider's wonders for himself.
Lord Tywin had put an end to that hope ten days before his dwarf son's sixteenth nameday, when Tyrion asked to tour the Nine Free Cities, as his uncles had done at that same age.
A Dance with Dragons, Tyrion III
From the same passage we can see that he has seen the Valyrian roads:
Come moonrise, they were back in their saddles, trotting eastward under a mantle of stars. The old Valyrian road glimmered ahead of them like a long silver ribbon winding through wood and dale. For a little while Tyrion Lannister felt almost at peace. "Lomas Longstrider told it true. The road's a wonder."
We also know he has visited the Wall.
The largest structure ever built by the hands of man, Benjen Stark had told Jon on the kingsroad when they had first caught sight of the Wall in the distance. "And beyond a doubt the most useless," Tyrion Lannister had added with a grin, but even the Imp grew silent as they rode closer. You could see it from miles off, a pale blue line across the northern horizon, stretching away to the east and west and vanishing in the far distance, immense and unbroken. This is the end of the world, it seemed to say.
A Game of Thrones, Jon III
However, I'm not sure what other Wonders he has seen/been too. He even actively turned down going to Qarth to see the walls.
"We could sail to Qarth," Penny went on. "The streets are paved with jade there, my brother always said. The city walls are one of the wonders of the world. When we perform in Qarth, gold and silver will rain down on us, you'll see."
"Some of those ships out on the bay are Qartheen," Tyrion reminded her. "Lomas Longstrider saw the walls of Qarth. His books suffice for me. I have gone as far east as I intend to go."
A Dance with Dragons, Tyrion XI
However, that doesn't mean he doesn't want to see the rest of the Wonders still. Do we know what other Wonders/Wonders Made by Man Tyrion has visited?