As I know, Mac and Quicktime support MOV/MP4 video well. There are many online apps can do the video conversion for you, such as zamzar, Acethinker Video Converter, mediaconverter, etc. They are totally free, and you don't have to download or install anything. Compatible with both Mac, Windows and Linux. Take Acethinker as sample, here are the steps to convert video.
1) Open your web browser and visit the Acethinker Video Converter, you can google search for it.
2) Click 'select files to start', locate your AVI or MKV video and add it into the app
3) Select MOV or MP4 as output format in the Format drop-down list.
4) Click Convert button and select a folder to save your converted video
5) Click Start to run the conversion, that's all.