How to use Apex Repeat with Set Collection in Salesforce?

You can definitely use a Set in a repeat.

In the Controller. The property and initializing it in the Constructor, for example's sake:

public with sharing class TestController {
public Set<String> aset { get; set; }

public TestController () {
aset = new Set<String>{'a','b','c'};
}
}

The Visualforce snippet:

<apex:repeat value="{!aset}" var="a">
<apex:outputText value="{!a}"/><br/>
</apex:repeat>