, 2022

We call four-digit integers good if their digits consist of exactly two types of numbers.
First, the upper two digits of integers in $[2000, 2099]$ are $20$. So the only good integers in the range are $2000$, $2002$, $2020$, and $2022$. But all of them are less than or equal to $2022$.
Second, the upper two digits of integers in $[2100, 2199]$ are $21$. So the only good integers in the range are $2111$, $2112$, $2121$, and $2122$. Since $2111$ is not divisible by three, and $2112$ is divisible by three, the answer is $2112$.