This seems like a quiz type of problem rather than real-world -- why would you want to force contacts to be located at their company's primary location? And if you're forcing an address and city, shouldn't state and postal code be included?

All that aside ... maybe something like this?  
I know some people like to make their handler more generic and just call an "AfterUpdate" handler method. I prefer to see what is being done when I look at the trigger itself. Also, best practice would be to only update the contacts that need to be updated -- the ones whose street or city differs from the account street or city. 

(I haven't compiled or tested this, so there could be typo's.)

trigger ContactUpdate on Account (after update) {
	if (trigger.isAfter && trigger.isUpdate) {
		AccountTriggerHandler.UpdateContactAddrFromAccount(Trigger.newMap);
	}
}


public class AccountTriggerHandler {
	public static void UpdateContactAddrFromAccount(Map<Id,Account> mapAccount) {
		List<Contact> listContact = AccountContactHelper.ContactsForAccountIds(mapAccount.keySet());
		List<Contact> updContacts = AccountContactHelper.ContactsNeedingAddressUpdate(listContacts, mapAccount);
		update(updContacts);
	}
}


public class AccountContactHelper {
	public static List<Contact> ContactsForAccountIds(Set<Id> acctIds) {
		return [
			SELECT MailingStreet, MailingCity, AccountId 
			FROM Contact 
			WHERE AccountId IN : mapAccount.keySet()
		];
	}

	public static List<Contact> ContactsNeedingAddressUpdate(List<Contact> listContact, Map<Id,Account> mapAccount) {
		List<Contact> rtnContactList = new List<Contact>();
		for(Contact con : listContact) {
			Account acct = mapAccount.get(con.AccountId);
			if (acct.BillingStreet!=con.MailingStreet || acct.BillingCity!=con.MailingCity) {
				rtnContactList.add(new Contact(
					Id=con.Id, 
					MailingStreet=acct.BillingStreet, 
					MailingCity=acct.BillingCity));
			}
		}
		return rtnContactList;
	}
}