Continental Ultra Sport II in 700x25 were barely larger than the 700x23. No problems clearing the frame and rear brake bridge on my '89 Ironman. Very under-regarded tires, especially for the low price. Not quite up to the ride of my 2015 or so Schwalbe One V-Guards, but not far from it either for a fraction of the price. And the cheap Contis are more puncture resistant and durable, while still being grippy on fast curves and moderately wet pavement.
But the Conti Grand Prix Classic (the handmade skinwalls) rubbed the rear brake bridge until I wore it down a bit on the indoor trainer and a few outdoor rides. It'll still scrape very slightly when I run through a puddle or wet dirt/gravel.