I am trying to upload a short animation I did in AE to Vimeo.
The video quality is very bad and the Vimeo staff said this my be attributed to my audio codec and they suggested I use AAC. I cannot find this option and have no idea on how to obtain this codec. Any help would be greatly appreciated.
Just for the record, MP4 is not a codec, it's a container - like AVI and MOV - that is often used for H.264 video and AAC audio streams.
MPEGStreamclip does indeed provide AAC audio, as do lots of other free and commercial encoding apps. Other popular freeware encoders that can do MP4 with H.264 and AAC are "SUPER" and "MediaCoder".
In fact, AE can also do this - if you choose the H.264 format in the Output Module you have the option for MP4 with H.264 with AAC using the Mainconcept codec. I can't say how the quality compares to other encoders because I've never used it, but it seems it can't do 2-pass encoding, which is usually used in high quality encodings.