What is a good reply to 1.d4 that will give me an open game?
1...d5. Tarrasch defense and, in general, c5 ideas practically always give an open game. As long as you can get in the move c5 with Black, you have excellent practical chances of achieving an open game.
Some sample variations -
[FEN "rnbqkbnr/pppppppp/8/8/8/8/PPPPPPPP/RNBQKBNR w KQkq - 0 1"] 1. d4 d5 2. c4 (2. Nc3 Nf6 3. Bg5 (3. Bf4 e6 4. Nf3 c5) 3... c5) (2. Nf3 e6 3. g3 (3. e3 c5) 3... c5 4. Bg2 Nc6 5. O-O Nf6 6. c4 dxc4 7. Qa4 Bd7 8. Qxc4 b5 9. Qd3 Rc8) 2... e6 3. Nc3 c5 4. cxd5 (4. Nf3 Nf6 5. e3 Nc6 6. a3 a6 7. dxc5 Bxc5 8. b4 Bd6) 4... exd5 5. Nf3 Nc6 6. g3 Nf6 7. Bg2 Be7 8. O-O O-O 9. Bg5 cxd4 10. Nxd4 h6 11. Be3 Re8
There is a recent book on 1.d4 d5 2.c4 c5 by Alexei Bezgodov. The idea is to liquidate the center pawns and get an open game. Inspired by the book I play it a lot as Black in my online blitz games with good results. Check out https://www.newinchess.com/the-double-queen-s-gambit
I personally like 1. d4 Nf6 because there are much more openings and traps white can use on black if he does 1. d4 d5.(for example Queen's Gambit) Plus, you can use the Budapest Gambit (which I really like) if the opening is 1. d4 Nf6