Assuming that I'm not accessing any inappropriate or dangerous sites, is it inappropriate to use my company's VPN for increased security when I'm connected to a public WiFi network on my personal computer?
I'm assuming that using the internet for personal use is fine in principle (for example during lunch break, before or after work, or just accepted use), and the question is just about "using company VPN".
If I was the IT guy, I would rather that VPN is permanently turned on instead of being turned off for personal use, and then you forget to turn it on. And the cost to the company will be quite close to 0.
In reality it is a question to ask your manager. If the manager allows it, it is fine, if not, it is not fine. Without asking, doing something that could be interpreted as inappropriate always carries the risk that it will be used against you if the company needs something to use against you. Even if there is no real problem.