Zuko always thought of Toph as his closest friend.
During the war, she was the first to welcome him and even though he accidently burnt her feet, she didn't treat him like he was a criminal…or a prince for that matter. He always loved how she didn't care who someone was and instead, treated everybody in whatever way she felt like doing. Which most of the time happened to be pushing others around like a Melon Lord. It was a welcome change from the high expectations of the rest of the Gaang and the pressure to end the war. Perhaps it was because Toph wasn't there to see him hunt down the avatar. Or maybe it was because Uncle Iroh liked her. Whatever the reason, all Zuko knew was that Toph was possibly the most interesting person he had ever met. That was why when he found out that she was curious about fire (that being the only element which she could not touch), he trained until he could produce a flame that was cool enough to be touched. He swore that the smile on her face when she finally 'discovered' fire was bigger than Sokka's when he found meat.
Once the war was over though, Zuko grew too busy to even see Aang himself. The first few years as Fire Lord were the times where he could only see the Gaang if he organized diplomatic visits to the Fire Nation Palace. Fortunately, Toph grew bored of staying in the Earth Kingdom and decided to travel. The Water tribes were to cold and she was blind (which was a pity because she loved penguin sledding). The Air temples (Aang had worked with Teo to clean them up and now lived there) were too high up and Aang was too busy to spar so she avoided those too. Kyoshi island was nice except that everyone kept badgering her to teach even though she wanted to lay in mud all day long. And so, Toph finally ended up in the Fire Nation Palace. Sure the palace was big enough to get lost in but that was what Toph loved about it. It was a constant challenge to find her way out of the long corridors and she frequently visited the war prisoners if only to taunt them. Most of all, she couldn't resist the Fire Nation simply because Zuko was the only one who never turned down her sparring challenges. When Zuko was busy, Iroh would take long walks with her and talk with her (these were the only times that Toph was silent). Toph decided to stay. For her, the Fire Nation was amazing- the food was scrumptious, the activities were fun and the taunting was priceless. For Zuko, Toph was the only one who when with, enabled him to completely forget all his duties and just be normal (or as normal as two immature, violent adults could be). Having Toph in the Fire Nation was the best gift he could ever have.
And so, the Blue Spirit and the Blind Bandit were the greatest friends in all four of the nations (only in secret though. They liked to deceive others- Zuko was boody in front of everyone else and Toph was a no nonsense tomboy. Not exactly a good match of friends) and each of them was grateful beyond measure for the friendship of the other.
This was precisely why, when Toph's birthday came up, Zuko gave his best friend the most incredible gift ever. He gave her a small island (previously a Fire Nation Colony but abandoned due to the frequent earthquakes) all to herself. When he told her that she could do whatever she wanted with the island, diabolical plans and all, she confirmed what she had sort of known all along.
Toph now knew that Zuko was most definitely her best friend.