Bianchi: Continental 28mm, which are actually closer to 25-26mm. I would use true-to-size 28s, such as Specialized, but they won't.
Other road bikes, with more generous clearance: 32mm (true size) seems a good number, 35 if they'll take it (Capos, Carlton).
Peugeot UO-8 transportation beater: 27x1-1/4" rear, 700Cx28 front. Because of my shorter-than-OEM fork offset, toe-to-tire overlap becomes even more severe with a 27" front or a 700Cx32-35 front, and that's with shortish 165mm cranks.
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"Far and away the best prize that life offers is the chance to work hard at work worth doing." --Theodore Roosevelt
Capo: 1959 Modell Campagnolo, S/N 40324; 1960 Sieger (2), S/N 42624, 42597
Carlton: 1962 Franco Suisse, S/N K7911
Peugeot: 1970 UO-8, S/N 0010468
Bianchi: 1982 Campione d'Italia, S/N 1.M9914
Schwinn: 1988 Project KOM-10, S/N F804069