I've had luck with basil, lettuces, parsley and mint. If you choose mint, be sure to grow it in a pot or it will overtake your garden! Basil has grown really well for me. It grows fast enough that I can harvest daily.
I've had a total bummer with mint, and lettuces are puny for us, but our land isn't fertile anyway.
I've had the best luck with different sorts of dill-for me they grow better than anything else; so much so that it is harvestable daily. It is also not very needy, just water and sunshine. I was lazy with weeding and it still grew lile crazy.
My favorit veggie I grow for me and my rabbits is Topinambur (Jerusalem Artishocks). Very good yield per m² even in not the best soil, and for me there is the additional benefit that it provides shade for the hutch area (grows up to 4m tall). All greens that I don't need are great food, and through winter I feed the tubers.
It's very easy to grow, almost no maintanence (just covering the ground with wasted hay from the hutches in fall and spring).
We're actually growing our own veggies for our rabbits as well. We've had success with Kale and basil. Especially basil. We're growing them indoors in our spare bedroom. Plus we're growing grass. Erlong LOVES the oat grass we grew for her.