Personally, I eat turkey hot dogs, but I don't know if that is an option for you. I get the ones that are 99% fat free and made from white meat only. They're 45 cal per dog.

home-cooked cheeseburgers are great, as long as you make fat allowances for the cheese. 

Burgers made with 1/2 ground turkey and 1/2 lean ground beef.  I prefer them with cheese, but they would be healthier without it.  If you really want good flavor, mix in some steak sauce or a packet of Lipton onion soup mix.

On edit:  Sorry, I just realized that you didn't indicate you would making these yourself.  The healthiest option, IMO, at a cookout is the burger, no cheese or mayo, but plenty of veggies if available.  If salsa is around because of chips or something, that is a great addition for some good flavor. 

well i guess it depends on if you have control over whats being cooked. If so, i would choose a lean beef such as turkey or chicken burger, topped with fat free cheese on a wheat bun (this is what i indulge in! yum). ketchup/mustard okay.

If not then i would say get the burger, blot off the grease, and no cheese

If there are any veggie burgers or hot dogs, go for those. They have almost as much protein, and way less calories and no fat. A veggie hot dog is around 80 to 100 calories, and a veggie hamburger pattie is 70 to at most 150 calories.

I always make my own burger patties... BBQ time means lots of different invitations so I jumble it up a bit... I usually make a batch of smaller size burgers (so that everyone gets a little taste:-)) and bring them with a crispy leafy salad... or some kind of a fruitsalad for desert... as a contribution

I use various base "meats":

quorn mince, lean beef, turkey, chicken, lamb... sometimes I also do a mix- lamb and beef for example.

My basic recipe for 1pound meat is:

2 onions- cooked in a tbs olive oil until clear and soft (don't brown them.
Mix in a huge handful of fresh chopped parsley and chives (I also like to add some fresh oregano sometimes)
a good squeeze of mustard
2 slices of bread crusts removed- soaked until soft and excess water squeezed out.
1 egg
1 pound ground lean meat.
salt and pepper to taste

Mix well until really combined and form patties- these freeze really well!

Whenever I have a BBQ, my roommate and I always buy the lean 94/6 hamburger (94% beef, 6% fat).  That or similarly lean steak.

Clearly a hamburger is the best option in this case, but if it is possible you could always bring along one of the suggested items (turkey burger, turkey hot dog, veggie burger, veggie hot dog) and talk to the cook ahead of time and let them know of your situation, they would be willing to accommodate you. 

Hebrew National makes a Kosher hot dog that is 97% fat free and tastes like the normal one.  I don't really like the texture of turkey dogs, but they seem to be highly recommended.  You can always get the morningstar chix patties or a veggie burger too.  I can get 95% lean, grass fed hamburger at my co-op.  When I do burgers, they are made of that.  There are also some flavored chicken and turkey burgers in the frozen foods.  I got some Chili/Lime ones from Trader Joe's that are tasty as heck.  Personally, if you don't eat five of them and don't go crazy with mayo based salads I think you could have any of them with little concern.