I stayed at with the company that Travelbug suggested- Oasis Collections- www.oasiscollections.com and they were wonderful, and just like bairesapt explained, so much more value for your money.
hey ernie- in three days you can definitely see everything there is to see in BA - the one thing you will be missing out on is eating at all the amazing restaurants - unless you want to try and fit a restaurant in every three hours.