Aconcagua (6962 m) would fit the bill, but the permit is not cheap.
Also (accessible by public transport):
Ojos del Salado-Argentine summit (6893 m)
Tres Cruces (6748 m)
Incahuasi (6621 m)
El Muerto (6488 m)
San Pedro (6145 m)
Queva (6140 m)
Chachani (6057 m)
I don't think peaks such as the mentioned Llullaillaco have public transport (?).
Many, many peaks (probably hundreds) in the over 5000 meters are in South America that would fit the bill. Many in Nepal and other areas in the Himalayan region as well. Lenana Point in Kenya too. Kili is pretty expensive.
In North America, La Malinche and Nevado Toluca can easily be done by public transport, though the highest summit of Toluca requires some scrambling. Both are higher than any peaks in the lower 48.
Is Elbert doable by public transport?
Leadville Hostel (when they aren't too busy) does shuttles to Mt Elbert.
none of the other Colorado fourteeners appear to have public transport as far as I'm aware.
Eolus, Windom, and Sunlight have public transport. You can easily fly or bus to Durango and take the train to Needleton. All three are just under the height of Pikes though.