I Must Garden has a long list of plants "not usually eaten" by rabbits.
It's broken down into categories including: annuals; perennials and bulbs; woody plants; vegetables and fruits; and herbs.
Since you asked specifically about vegetables, the only one in addition to J. Musser's list is Asparagus.
gardening.stackexchange.com/users/7305/Sue Saddest Farewell TGO GL
Really, rabbits are far less picky than humans when it comes to eating plants, so there aren't many that no rabbits eat, that we would.
However, there are a few that rabbits generally avoid (at least for me): Vegetable Beds: Tomato Squash Cucumber
most melons (they eat watermelons here) Corn (needs protection when young, but grows tall) Sunflowers (needs protection when young, but grows tall) Peppers, normally.
One time a rabbit kept eating the plants of someone I know, so this one's debatable; depends on the variety and the rabbit.
Potatoes Onions (usually, especially strong ones) Garlic Leeks Artichokes (only because they're spiny
; hungry rabbits will eat them if there isn't anything else
Many herbs Rhubarb Woody Fruit: The genus rubus (brambles) because of the spines.
Thorny gooseberries (trained high - rabbits eat the leaves) Juneberry ( Amelanchier )
I don't know very many fruit plants they won't gnaw, but some berry plants can be trained as a standard, and a vinyl tree guard (or similar) used to keep them from gnawing.
Where I am (and you aren't), you have to protect the trunk much higher than you'd think, because in winter (when they're eating bark), they can walk on top of whatever snow may be on the ground.
Again, probably not a problem in Texas, but I'm including it to be less localized.
gardening.stackexchange.com/users/419/J. Musser
I have a vegetable garden in Renton, Washington, with tomatoes, corn, peppers, squash, melons, peas and beans.
I also have a recently noticed rabbit.
It's not a wild rabbit; I can tell by the coloring (I once raised rabbits).
So far, I haven't noticed any nibbles on my veggies.
I even bought some food for him/her which hasn't been touched.
Oh, well, the deer will probably find it and dispose of it.
gardening.stackexchange.com/users/11691/Rose Rawson
They don't like eating bitter stuff, either - and there's quire a bit of that.
Collards can be rather bitter - though delicious - and so can kale [though there is sweet kale].
Some heirloom lettuces are quite bitter - we picked some lettuce seeds up in Italy once that only could be eaten young since they got bitter as they aged.
So, the lesson is that "sweet" varieties of greens might be worse at keeping rabbits out than the older, more bitter heirloom varieties.
Pungent and aromatic plants also deter rabbits, everything from most herbs to geraniums to onions.
"Pungent" includes "hot," and that includes mustard greens.
I have some baby bunnies living in my garden now, and they are blessedly not eating much -
but the garden is mostly herbs, tomatoes, peppers, and greens such as collards and mustard.
They have nibbled the eggplant leaves, but not much
- I sampled a leaf and they are slightly bitter too!
gardening.stackexchange.com/users/21961/Kenneth Childers
Iv got a rabbit and she lives in my garden most of the time, as long as they are mature she avoids the strawberries.
When the plants are small she'll mow them off, but once mature tends to leave them alone, this seems to apply for dahlias too, once it's big
she ignores it but will eat new growth or shoots.
gardening.stackexchange.com/users/17430/Iain Simpson
They never touch my Swiss chard.
gardening.stackexchange.com/users/25776/jan
That's a great question, and one many gardeners face sometime along the line.
No matter whether you think bunnies are cute or a total pest, it's important to safeguard against rabbits, because if you don't, they'll clean your garden dry.
If I were you, I'd think less about types of plants rabbits will avoid and more about your infrastructure...as in, how to create a rabbit proof garden that will allow you to grow whatever you want and look attractive in the process.
There are numerous resources out there that focus on improving your garden design and helping you to eradicate the problem before it even reaches your garden.
However, if you don't want to take this route, check out this great Better Homes and Gardens article answering your question.
It mentions some plants that rabbits tend to stay away from, including Alliums, anise hyssop, daylilies, bee balm, catmint, lavender, yarrow, and other plants that may or may not be edible, with details on each.
gardening.stackexchange.com/users/14739/Alex Kuchel
I have an area for a few raised beds were it would be impractical to secure against rabbits. What can I plant there that they won't be interested in?  I'm assuming they won't eat any berry types, but what about newly planted tomatoes and other kinds of vegetables?
What vegetable/fruits plants will rabbits not eat?
gardening.stackexchange.com
<vegetables><plant-recommendations><pests><fruits><rabbits>
gardening.stackexchange.com/questions/14929
gardening.stackexchange.com/users/3473/Philip
You should avoid asparagus, tomatoes, squash, cucumber and strawberries. You should be fine with swiss chard and anything with bitter tasting leaves. Rabbits tend to avoid tomato, squash , cucumber, Swiss chard and asparagus as well as strawberries. They generally don't like eating bitter stuff. Rabbits also tend to stay away from Alliums, anise, hyssop, daylilies, bee balm, catmint, lavender, yarrow.
Rabbits tend to avoid tomato, squash , cucumber, Swiss chard and asparagus as well as strawberries. They generally don't like eating bitter stuff. Rabbits also tend to stay away from Alliums, anise, hyssop, daylilies, bee balm, catmint, lavender, yarrow.