We drove through Forks this summer. It seemed like a nice little town - no sign of vampires or werewolves, but we were through there during daylight hours.
Forks is a small town out on the Olympic Peninsula. Great place to stay if you like walking on beautiful rainy/cloudy sandy beaches, hiking through rainforests, and eating lots of salmon. Get away from it all, only a few hours from Seattle, via ferries, a little longer to Victoria.
Only missed 'Twilight' and 'Fault in Our Stars'. The latter I had no idea, the second I had a general sense it was in the Pacific Northwest, so tried Seattle and Portland and then gave up.
"where these books took place": this is going to be hard to define. Anna Karenina definitely also involves Moscow and country estates far from the cities. Big up for Joe Wright's film version, one of the best films I have ever seen.