Wrexham, preparing for a second successive season in the Championship, meet Leeds in Tampa on Sunday, 26 July before facing Liverpool in New York four days later.
Their final pre-season game is against Sunderland on Sunday, 2 August in Philadelphia and Vyner is looking forward to make an impression on tour.
“I’m ready to go, I feel good, I feel fit,” Vyner added.
“These tours, and pre-season in general, are for everyone to essentially give the manager a headache.
“I’m looking to do that and hopefully have some more games, get some more minutes, get myself fitter and just be ready for the season.”
Vyner, 29, joined Wrexham from Championship rivals Bristol City for an undisclosed fee during the January transfer window.
He had a toe injury when he joined and was then thrust into action in central midfield. He missed the final five games of the season with a groin injury.
“I went away in the summer and there’s a lot more to come,” Vyner said.
“When you move to a new club, and it’s the first time I’ve done that on a permanent basis, it is about getting to grips with everything off pitch as well.
“There’s a whole bunch of stuff that goes on behind the scenes that people don’t really see.
“Just bedding into a new place, new club and a new changing room, is a big jump.
“I feel now a lot closer to the lads and everyone’s been great, but getting a lot closer naturally and getting to know each other’s personalities, playing styles, everything, takes a bit of time.
“I’m ready to go and there’s a lot more to come.”
