Individual daily MODIS scenes can be obtained at the Level 1 and Atmosphere Archive and Distribution System (LAADS) at: https://ladsweb.nascom.nasa.gov/search/. The page should open with the 1 Products tab active. In the upper left specify the appropriate sensor(s); Terra, Aqua, or Combined. Then select the MODIS Collection. Currently the most recent is Collection 6.
Below this look for the section Level-0 / Level-1 and click on MODIS Terra, Aqua. This brings up a list of MODIS daily scenes on the right. Select the Level 1B Calibrated Radiances dataset at the spatial resolution you wish.
Click on the 2 Time tab and enter a single date or date range. Normally for Coverage Selection you will select only Day.
Next click on 3 Location and use one of the methods to define your region of interest.
Finally click on 4 Files to make a final image selection.
View the browse images of the datasets that meet your search criteria. After you select the dataset(s) you need, lick the Get Data icon on the bottom toolbar to download your image(s).