I am 3-1/2 months into a year-long trip around Europe. I'm averaging about 4 miles per day (with frequent 6- to 8-mile days), on all kinds of terrain. I have been very happy with my New Balance Minimus 10v1 trail runners from REI:
https://www.rei.com/product/110824/new-balance-10v1-minimus-trail-running-shoes-mens
They are not for everyone, of course, but they have worked well for me. I am a woman, 6' tall with size 13 shoes (B with a AA heel, low volume--think swim fin), so buying shoes at all is tough, and athletic shoes always seem so bulky (and garish with their white soles, bright colors and sparkle). I was glad to find these, as they fit like a dream, are (almost) all black, and have a low profile. They are lightweight, as well. They have a Vibram sole, and I think they look like the mitten version of those awful five-finger shoes. They are not waterproof, but they gripped the hell out of the wet rocks at Gullfoss and the few wet boardwalks we've encountered. They do make them for women--not in my size, of course, and not in all-black.
After more than 400 miles, the sole is getting worn down. I've been using gel insoles to extend their life, but with the winter coming on, I will need to replace them. I will buy the exact same shoe again. As soon as I can find them over here! If anyone knows of a running shoe or outdoor store in Madrid or Barcelona that might carry them, please let me know. It's hard to get stuff shipped when you're on the move every week or 10 days.
I don't have any affiliation with REI (other than being a member) or New Balance, and I will not get any financial gain if you click through to REI and buy these shoes.