Good question in my opinion. Yes, play the Grunfeld but don't play d5 until white has placed his knight on c3, usually a move or two later. In the meantime you can play Bg7 and 0-0 as useful waiting moves. Once Nc3 comes (as it usually does), play d5 straight away unless you want white to play e4 and find yourself in a Kings Indian. The advantage of delaying d5 for black until white plays Nc3 is in the Exchange Variation (cxd5 Nxd5, e4) when you will want to exchange your attacked knight on d5 with his/hers on c3, after which your bishop on g7, the immediate advance c5, and the arrival in due course of your rooks to c8 and/or d8, offer black good potential for counterplay. If you play d5 before white has played Nc3 there isn't a particularly good square for your knight attacked by the white pawn's advance to e4 in my experience and of course there won't be a white knight then (on c3) with which to exchange your own horsey.
In short only play d5 to initiate the Grunfeld after Nc3 and then play it immediately. See an exemplary sequence of moves directly below.
You may find that white doesn't go for the Exchange Variation with cxd5 anyway, but if that's the case you haven't lost anything by delaying d5 until white's Nc3, as the waiting moves Bg7 and 0-0 would be on your to-do list anyway.
Is it a good idea to play it against Nf3 instead of the more common Nc3?
Or is it better to play a King's Indian Defence and play the two together like how the Nimzo-Indian and the Queen's Indian are to be used together?