If you want to use the <apex:detail/> tag to display the Account, that would be the easiest - however, there is not a standard way to attach a behavior to a dropdown with in that page.

Here is an example of a solution using a custom drop down list:

VF PAGE

<apex:page standardController="Account" extensions="OpportunityFilter">
    <apex:form >
        <apex:selectList value="{!regionValue}" size="1">
           <apex:selectOptions value="{!regionOptions}"/> 
        </apex:selectList>
        <apex:commandButton value="Update Opportunities" action="{!updateFilteredOpportunities}"/>
    </apex:form>
    
    <apex:pageBlock >
        <apex:pageBlockTable value="{!filteredOpportunities}" var="opportunity">
            <apex:column value="{!opportunity.name}"/>
        </apex:pageBlockTable>
    </apex:pageBlock>
</apex:page>

CONTROLLER

public with sharing class OpportunityFilter {
    public String regionValue {get;set;}    
    public List<SelectOption> regionOptions {get;set;}
    public List<Opportunity> filteredOpportunities {get;set;}
    
    public OpportunityFilter(ApexPages.StandardController controller) {
        regionOptions = new List<SelectOption>();
        regionOptions.add(new SelectOption('Manufacturing','Manufacturing'));
        regionOptions.add(new SelectOption('Medical','Medical'));
    }
    
    public void updateFilteredOpportunities() {
        filteredOpportunities = [SELECT id,name FROM Opportunity WHERE Account.Industry = :regionValue];
    }

}

This uses a query on the Account Industry field, but you could adjust to filter on a custom "region" field quite easily.

Hope this helps!