I am taking advice from this website. If you want to train your Kadabra, you should train in Iron Island mainly (from the website), despite being extremely inaccessible. But, be warned of the Graveler there, they can Selfdestruct! Besides, those Pokémon might not be much of a challenge for you thanks to Kadabra's high Special Attack stat. If you don't like Iron Island, you can train at routes 218 or 221. Once those Pokémon get to level 33ish, you can start training at Acuity Lakefront and Route 217. By level 35, all of your Pokémon can begin training at Mt. Coronet 2F. If the wild Pokémon there don't help, you can use the Vs. Seeker at some places; some of the trainer's Pokémon may get into the 30s where you are. Trust me; the Vs. Seeker will help you. It assisted me in my training for the Elite Four in Platinum; it'll help you! But, not every trainer has a higher-leveled team in Diamond compared to Platinum (my game of expertise). So, go with those places or Vs. Seeker.
Let me know if you have any problems. I hope this helps!