Applebee’s has a great food allergen menu on their website (if that link breaks, go to their main site – there is a link at the bottom of the page to their food allergen chart).
I’ve eaten there with success as they do have quite a few options, and I had good luck with a well-educated staff. I’ve received equally rave reviews of Applebee’s from Go Dairy Free viewers, too. Please be aware though that most of the dairy-free options are meat or seafood entrees; I did not see many vegan options on the menu, but I’m sure that they can accommodate by customizing a dish.
See the website below for menus, locations, etc.