<aura:iteration items="{!v.contacts}" var="contact" indexVar="studentNo">
    <li class="minli">
        <div class="studentPhotoDiv"><ui:outputRichText value="{!contact.Photo__c}" class="studentPhoto"/></div>
        <div class="studentNameDiv"><ui:outputText value="{!contact.Name}" class="studentName" aura:id="studentName"></ui:outputText></div>
        <div class="studentNameDiv"><ui:outputText value="{!contact.Id}" class="studentName" aura:id="studentID"></ui:outputText></div>
        <div class="studentSelectDiv"><ui:button label="Check-in" class="studentSelect" press="{!c.studentSelect}"></ui:button></div>
        <br style="clear: both;" />
    </li>
</aura:iteration>

var studentId = component.find("studentID").get("v.value");
console.log(studentId);