I've been a vegetarian for 24 years. It used to be almost impossible to find meatless meals dining out. All I could ever get was spaghetti with marinara sauce. Nowadays, it's getting A LOT easier. Many restaurants offer veggie burgers. I find that if I don't see anything vegetarian, I just nicely ask the server if there is anything without meat and they almost always either offer to make an existing dish meatless, or they'll offer to make something special just for me. I'm always sure to tip WELL when they do that for me.
After you get more used to being vegetarian, you'll start getting creative. I can scan a menu and quickly come up with a meatless dish, by combining piece from various entrees (for example, take the alfredo sauce from one dish and add it to pasta instead of chicken, etc). If I want to eat lighter, I'll check out the "sides" on a menu and combine them. For example, a baked potato, with steamed veggies and a side of pasta. I just build a meal, so to speak.
Also, when I do see vegetarian choices, I always make a point to tell a manager that I will be sure to return since they offer a vegetarian choice. That way they know what's selling and why. I've had small restaurants add vegetarian items just because of my feedback. One of my favorite places to eat is a BBQ Smokehouse restaurant that's ALL MEAT. I went in to use their bathroom one day, checked out their menu, and politely told them the restaurant looked nice but what a shame that they didn't offer vegetarian choices. The owner immediately took the challenge and made me a fresh veggie quesadilla. Now when I stop in, they all try to come up with new ideas and so far I've never been disappointed. They think it's funny that "the vegetarian" eats at their BBQ joint.
Wraps are another thing most restaurants can make with ingredients on hand. Mexican food is another great choice, veggie burritos, taco salad, enchiladas, etc can call be made meatless. Italian food is a good choice too. Pasta dishes are plentiful and easily altered to be made without meat. If you like eggplant, then Eggplant Parmesan with pasta and sauce is a good choice.
The best tip I can give you is to talk to the servers, managers, owners. I find they are almost always willing and eager to come up with a dish to keep you and the family coming back.
Good Luck and hang in there. It really becomes second nature after you get used to getting a little creative.