Answer: A robotic cat.
Currently the subject of an Indiegogo campaign, Nybble is a DIY robotic cat that could be a fun and easy way to learn a little bit of computer coding. Should the project be successful, $200 will get you a disassembled Nybble along with a motor board and detailed instructions for assembly.
However, if you happen to have access to a laser cutter, you may be able to build your own Nybble for free. The cat is entirely open source — you just need to be able to cut the pieces for its wooden frame.
Once the cat is built, you can program it to do a variety of things including walking and playing. Additionally, you can add a computer chip like a Raspberry Pi once the cat is built so it can do more complex things and maybe even start to think a little bit.