Red Robin has several vegan options. Their website has a really convenient tool that lets you adjust menu items to make them vegan. You have the option to select a specific location and if possible cross contamination is ok. Each location is different so this is a great way to make sure what each location has that is vegan.
Some vegan items are a Veggie Burger, Impossible Burger, salads (need to modify to be vegan), Bottomless Steak Fries, Bottomless Steam Broccoli, Bottomless Sweet Potato Fries, and Bottomless Yukon Chips.
https://www.redrobin.com/allergen-menu
Red Robin has Washington state locations in Auburn, Battle Ground, Bellevue, Bellingham, Bonney Lake, Bothell, Burlington, Covington, Des Moines, Everett, Federal Way, Kennewick, Kent, Lacey, Lakewood, Lynnwood, Marysville, Monroe, Olympia, Puyallup, Redmond, Renton, Seattle (Northgate), Silverdale, Spokane, Tacoma, Tukwila, Vancouver, Wenatchee, Woodinville, and Yakima.