As I believe it is only fair to provide my full solution now that I have benefitted from input, here is the full code for the trigger I just completed.  Also, even though this post will be marked as the solution post, I will make sure that mcrosby gets the Kudos.  Thanks again!

/**
    TRG_SurveyFeedback_UpdateParentAccounts
    
    @description
    Adds/Updates the Parent and Ultimate Parent accounts for the 
    Related Account on the survey results.
    
    @author Jeff Bloomer
    jeff.bloomer@standardregister.com
    937-221-3513
    
    @version 9/24/2013
*/

trigger TRG_SurveyFeedback_UpdateParentAccounts on Survey_Feedback__c (before insert, before update) {

    Set<ID> setAcctId = new Set<ID>();				//Holds the Account Id from the Survey Feedback			
    List<Account> currentAccount = new List<Account>();		//Holds Related Account on Survey Feedback
    List<Account> parentAccount = new List<Account>();		//Holds list of Parent Accounts for Related Account
    String relAcctId = '';						//Related Account Id
    Integer topAccount = 0;						//Holds number of top-most account in parentAccount list
    Boolean boolParentAssnd = false;				//Is Parent Account Assigned yet?

    //Upon the addition or update of a new Survey Feedback
    //record, obtain the Id of the Related Account (Account__c).
    for (Survey_Feedback__c sfb: Trigger.new){
        setAcctId.add(sfb.Account__c);
    }
	
    //For the Related Account in setAcctId, obtain the Account Id and Name.
    currentAccount = [SELECT Id, Name FROM Account WHERE Id in :setAcctId];
    //Assign Account Id to a string variable to use in the getAccountHierarchy function below.
    relAcctId = currentAccount[0].Id; 
	
    //Get the list of Accounts in the hierarchy for relAcctId.
    parentAccount = getAccountHierarchy(relAcctId);

    /**
	getAccountHeirarchy(string)
	
	@description
	The getAccountHierarchy function, which requires an accountId as a paramenter,
	fetches the list of accounts appearing above the accountId in he hierarchy.
	It returns a list (accList) that contains the following information for the Account:
	
	Id, Name, ParentId, and Location_Type__c
		
	@author Michael Crosby
	michael.crosby@newedge.com
    */
	
    List<Account> getAccountHierarchy(String accountId){
		
	List<Account> accList = new List<Account>();		//Holds list of accounts above accountId
        Boolean isTop = false;					//Is this the top-most account?
        
        //Until the top of the hierarchy has been reached,
        //populate accList with the accounts above accountId.
        while (!isTop){
            //Get the Id, Name, ParentId, and Location_Type__c for accountId
            Account a = [SELECT Id, Name, ParentId, Location_Type__c FROM Account WHERE Id =: accountId limit 1];
            //As long as the ParentId field is not blank, assign it to accountId
            //for the next time this loop returnes to the query above.
            if (a.ParentId != null){
            	accountId = a.ParentId;
            }else{//Otherwise, the top of the hierarchy has been reached
            	isTop = true;
            }
            //Append the account information retrieved to accList.
            accList.add(a);
        }
        return accList;
    }
    //End of getAccountHeirarchy
	
    //Get the index of the top-most account in parentAccount
    //Note: because array indexes always start with zero, the
    //last index number will be one less than its size.
    topAccount = parentAccount.size() - 1;

    //Now that the hierarchy list has been fetched, populate
    //the Parent__c and Ultimate_Parent__c lookup fields with
    //the pertinent information.
    for(Survey_Feedback__c sfb: Trigger.new){

	//Step through parentAccount to find the first Parent
	//account and assign it to the Parent__c field.
	//Note: start with index 1, because index 0 is the Related Account.
	for(Integer i = 1; i < parentAccount.size(); i++){
	
            //As long as Location_Type__c is Parent and this field has
	    //not yet been assigned during this process, populate Location_Type__c.
	    //If Location_Type__c is assigned in this step, change boolParentAssnd to true.
	    if(parentAccount[i].Location_Type__c == 'Parent' && boolParentAssnd == false){
		sfb.Parent_Account__c = parentAccount[i].Id;
		boolParentAssnd = true;
	    }
	}
	//As long as the top-most account is an Ultimate Parent and not 
	//the Related Account itself, populate Ultimate_Parent_Account__c. 
	if(parentAccount[topAccount].Location_Type__c == 'Ultimate Parent' && parentAccount[topAccount].Id !=  relAcctId){
	    sfb.Ultimate_Parent_Account__c = parentAccount[topAccount].Id;
	}		
    }
}