Another vote here for the Veloflex in 20s. I use their tubulars, which really render that classic look.
You can find Vittoria Graphene 2.0's in 23, which likely measure closer to 22, knowing their penchant to "oversize."
They put much larger graphics on their tires, though, so that might turn you off. Available for cheap, nowadays.
Some LBS's may stock old Continental Grand Prix's in 20 - non-foldable or foldable. Haggle the price downward.