My brother and I will be in in Brazil delivering medical supplies to villages on the Amazon River for 8 days. After this we will have 3 days and need help figuring out what to do. We looked at going to the beaches on the North East of Brazil but fear we will spend most of our time in route. Is this true? After our 3 days we will be flying out of Manaus to Sao Paulo then to NYC. Thanks for your thoughts!

Change your domestic flight. Fly from Manaus to Rio, which, yes, will take you most of a day. Spend your time exploring Rio, which has nice beaches right there in the city. Then it is a short flight or bus ride to S.P. to get your international flight.
If you can't change your flight out of Brazil, you'll have to settle for some activity near Manaus. There are plenty of jungle lodges you could go to from there. But if you want to do that with your short time, you should arrange something before you leave the USA for Brazil. If you wait until the last minute, you'll not have time even for that, because transport to a lodge usually takes half a day, all by itself.
The northeast of Brazil is totally out of the question w/ 3 days. Even Rio would be difficult.