Faction Symbols

[Jolt]

Pegasus was a symbol of Corinth. Another symbol very enjoyed by foreigners were overly public priestesses of Aphrodite. If you know what I mean.. :P
The patron of Rhodos was Apollo, to which the colossus was dedicated. The most frequent animal symbol of Rhodos was the lion.

[Teleklos Archelaou]

Pegasos is probably the most common symbol on all Greek coinage. A depiction of Zeus may be first really, or Athena, but Pegasos can nicely be used as a generally recognizable emblem of many Greek poleis and doesn't immediately make you think of any one kingdom (though you are right that Corinth may be the best known polis that commonly used it).