Advice Best Shoes for a Month-Long Europe Trip?

I will be leaving for a month trip to Europe in 11 days and I'm looking to buy a new pair of shoes. I'll be visiting Spain, Switzerland, Italy, and Greece, so I need something versatile that can handle city walking, light hiking, and maybe even a bit of rain. I'm torn between getting a pair of sturdy sneakers or something more like a hiking shoe. What shoes have you found to be the best for long days of walking and varying terrains? Any specific brands or styles you'd recommend for this kind of trip?