It really depends on whether you are recording to make money, or just for fun, whether you have lots or little money to spend on an AI, and whether you intend to buy a fantastic mic, a budget mic, or something in between.
I myself was about to purchase an audio interface to record audio to accompany my piano playing. However, I decided to buy a USB mic and am very happy with it. I purchased a Blue Snowball USB Mic, and have never looked back. If you have a spare USB port, I can certainly recommend getting such a mic, and saving a bit of cash as well!
Further, with the purchase of a Lightning-to-USB adapter or similar such dongle for other devices, I am able to use this Mic with my iPad and iPhone, whereas a non-USB mic might require a lot more setup and equipment to record on the go. The USB also ensures compatibility with almost all computers if travelling or in an unfamiliar setup.
However, if you intend on buying more mics, or more instruments with line-outs, then an audio interface could provide the added flexibility of being able to swap your mic for another or an instrument.