First of all, I have found, never to be afraid to ask a waitress if the chef can prepare something wonderful and non-dairy. Believe me, you won't be the first person to ask and many times, menus are set and chefs often get bored--they're looking to make things not on the menu and want an opportunity to try out something new. I imagine that some of the best meals are what chefs prepare for themselves in their own homes!
Asian foods: Always a safe bet. Far East food rarely, if ever, uses milk products, however, be careful about dim sum and other appetizers (crab-cheese wontons) that may contain butter or cream cheese.
Kosher fleishig: They serve only fleishig or only milchig food. Because observant Jews believe that millk and meat must not be eaten at the same meal, kosher meat products are milk-free. Don't confuse "kosher-style" with the real deal though.
Mexican foods: (not the fast-food kind) the sour cream and cheese is visible, so it's easy to avoid. Sometimes refried beans are prepared with milk, so make sure you ask. Also be aware that some Mexican (and other restaurants) might mix sour cream with their guacamole and one Mexican restaurant I like to go to, actually puts shredded cheddar in theirs, so I always have to ask for it sans cheese. Fajitas are always a safe choice.
French and Italian foods: Try to avoid. :( But some places may use olive oil instead of butter if requested to do so.
Indian foods: Another bad choice. They use a great deal of yogurt and ghee (clarified butter) in cooking.
Plain American foods: Is usually a good bet. You can typically see the milk products.
Grill restaurants: Ask the waitress to have the chef use oil instead of butter when cooking your chicken or fish or other meat dish.
Pizza joints: You don't have to fear when your co-workers invite you out for pizza! Good pizza places will accommodate you. Ask for a cheeseless pizza with veggies, or pesto, fresh tomatoes, even tofu. Chefs like to get creative--even with pizza. They might even offer soy cheeses--you just have to ask!!
Breads served in restaurants are usually milk-free and rye bread is nearly always milk-free. Whole grain breads are apt to be milk-free than are white breads. Avoid muffins and other quick breads.
Pass on appetizer dips. Stick to nuts or pretzels.
Clear soups are usually a good choice. If you like French Onion soup, ask for it without the mass of cheese on top. Or for Tortilla soup, ask that they don't put a dallop of sour cream and shredded cheese on top. Usually restaurant bean soups are prepared with milk, so make sure you ask.
Salads are typically a good option, but beware of the croutons. They may contain Parmesan and other milk products. But ask about pasta salads--sometimes they are made with an oil dressing, but there still may be chunks of cheese, or Parmesan cheese on it.
Avoid fried foods that have been rolled in crumbs or dipped in batter.
Sandwiches made with rye or French bread are usually a good choice. Avoid any kind of salad sandwich, as those usually are made with milk products, But potato salad is typically made without milk products.
It's a good idea to skip dessert unless plain fruit is available.
What are some of your restaurant tips for us non-dairy eaters?