How do I get the IP of the Salesforce Instance from which the callout is to be performed?

The Salesforce IP addresses can change, and you should use Salesforce IP Address to whitelist as a starting point.

With that taken into account, you can use an existing web service to tell you what the IP address is (for that request at least).

HttpRequest req = new HttpRequest();
req.setEndpoint('http://icanhazip.com/');
req.setMethod('GET');
Http httpReq = new Http();
HttpResponse res = httpReq.send(req);
System.debug(res.getBody());

Log output from na5.

10:09:49:424 USER_DEBUG [6]|DEBUG|182.50.78.8
Don't forget to add http://icanhazip.com as a remote site.