Space Research Institute is located in the south-west region of Moscow, Metro station: Kaluzhskaya.
Address of the Space Research Institute:
84/32 Profsoyuznaya Street
⇒ Printable Moscow metro map and information (8 MBytes PDF file download)
You should get off at "Kalyzhskaya" metro station using the southern exit number 6. After leaving a station lobby through glass doors you should go straight to the end of the tunnel, then take right and use the stairs to get to the surface. From this point you may follow either arrow on this map: (click image to enlarge)
Space Research Institute on Google Maps: