Rabbits are usually not limited in cities. I raised rabbits in 2 cities with strict pet limits and livestock bans.
It is not feasible to grow a significant portion of rabbit feed in a city. Rabbits may be small livestock, but require a significant amount of hay to grow.
I started with big dreams and rabbits in the city. I'm finally out on a farm with goats, sheep, chickens and starting a rabbit project.
With rabbits, the most sustainable way I have found is to get purebred pedigreed rabbits and breed them to show requirements. Depending on the quality of your stock and the popularity of the breed, selling some show rabbits can pay for feed and more. My pet quality rabbits sold for $60. In that breed, you can get up to $400 for a desirable show rabbit. In contrast, you might get $5 for a butcher-ready meat rabbit.
Buying used cages is less expensive than building cages. Stick with wire cages which you can flame sanitize.
Another citified livestock animal, guinea pigs. Apparently they're good little meat animals and there is pet and show markets as well. To find show guinea pigs, google "cavies". Another animal not limited in cities.
Good luck to you! I'll be following your adventures!
John Seymour's "Complete Guide to Self-Sufficiency" is a wonderful read that will give you lots of ideas too. I believe they've reprinted the book not long ago and "modernised" it a little.