Closing Vents In Basement

First year in this house. I have 24000 BTU of cooling from my A/C unit. The house is very small (main level and basement....total square feet, 1100) The unit is more than capable of handling the full load. There is no door between the main level and basement. 6 diffusers on main level and 4 in basement. 1 return air on main level and 1 in basement. With the warm weather just starting, the basement gets very cold (if the a/c is running) while its comfortable on the main level (other than one room at the end of the house.....furthest from a/c unit/furnace). My daughter sleeps down there and has her own living space so I have no choice but to shutoff and tape off the vents. Should I also block off the return air grill downstairs (or does it matter because there is no separation between levels anyway)?