Pegu

An easy trip by taxi from Rangoon is Pegu.

There is an amazing pagoda, similar to the Shwedagon in Rangoon. It is called The The Shwemawdaw (Shwe means gold).
Inside was a photograph of some interesting travel companions, Richard Nixon and John Connely, it was taken on a visit to the pagoda.

There is also, one of the largest reclining buddha images in SE Asia.

You will be an oddity, in Pegu, since not very many tourists go there.