Think in terms of greens rather than veggies. Basil, cilantro, green leaf lettuce, red leaf lettuce, romaine, parsley, spinach... are all options.
BUT you probably only want to get one of those. Any new green needs to be introduced very slowly to a rabbit. So you offer a little piece of something new. See if bunny will try it. If he won't try it, then try again each day for the next several days. Sometimes it takes several tries.
If he does try it the first day, great. Then the next day, you can offer a little bit more. Check for changes in poos. If all remains normal, then each day increase the amount of that same green. After 5 days or so of increasing amounts, by then you'll know that that can be added to your bunny's list of tolerated greens.
This is why I suggest only getting one green at the store to start. By the time you've gone through the 5-7 days with one new type, any others that you bought will probably be bad.