> not only do rockets need something to push against, they have to carry it with them
I think you meant "something to push with. But anyways, nuclear explosions make their own hot gasses out of the reactants, and the problem with that is getting that to be directed and also to not get the ship -you know- blown up in the process.
A better approach is to have a nuclear reactor to heat reaction gasses to much higher temps than chemical reactions allow for, thus increasing ISP a lot. The main problem with this is that nuclear reactors need a lot of cooling, even and especially after you shut them off, and the reaction gasses are going to be your only way to cool them. Alternatively you can carry huge radiators -- really huge, because in space you don't get to exchange heat with an atmosphere or a body of water, so you can only radiate or ablate away the excess heat, and either way would require huge amounts of extra mass. Another problem is that stop/start latency with nuclear reactors is huge, so they would only work for interstellar travel, I think. I'm sure if you carry enough reaction mass then nuclear reactors can work well for interstellar trips.