Use a con function. The con function will look at every pixel in the in_conditional_raster (the current raster being evaluated. If the pixel equals NoData is true, then replace that pixel with the value from the following day, if it is false (the pixel has data) do nothing. Here is a link to the Con tool. If your file names are something like 20021202 (YYYYMMDD) then it will be easy iterate though them. Of course it will get more complicated if the following day also has a NoData value. Happy coding!