What's the best meal to serve for my girlfriend and her parents. I need to impress them! Thanks.
I would pick something that you are already comfortable making, that is reliable and tasty. I wouldn't go too far outside your culinary comfort zone the first time out. I tend to "play it safe" when you're trying to impress the parents for the first time.
Maybe a roast chicken with potatoes?
Definitely a roast chicken. Or something that will fill the house with great aroma, so when they walk in, they will instantly love you. A chocolate cake wouldn't hurt either.
When I did this for my girlfriend's parents, I was the first guy they had seen cook outside of a restaurant or a grill so it was easy. I married their daughter and I still do all the cooking...
My recommendation is to go with what Valser says and keep it within your comfort zone. I would add that you want a menu with that you can perform some prep ahead of time and is forgiving. I think it is more important to demonstrate that you are able to keep control of the task while being sociable than it is to execute a technically or time challenging menu that is risky and may require too much of your attention. As someone that has to cook every day for 5 people, I am always happy to go somewhere and have even a simple meal prepared for me. I would do something straightforward that can be 'upped' at the end if you have the time and resource either by adding an additional flavor or presentation component.
I would start by asking my girlfriend what their food preferences/allergies are. Being mindful of those preferences can go a long way to establishing a reputation of being courteous. Then work as others have said within your culinary comfort zone as well was within the zone of entertaining.
My favorite way to cook for others and to participate in the socializing is to spread the meal in several courses. I serve on course, we sit together eat and enjoy. We clear the table, I work on the next. Mostly I have the courses timed so that I am putting final touches on the subsequent dishes. But it seems to turn into a very relaxing time for all and the food is served at it's best versus having to get all the timing down so that it all comes to the table at one time.
One of the easiest recipes I know and is always a hit with anyone who likes a fork-tender pot roast (my sister-in-law calls it "Idiot's Delight" but it really is good. Preheat oven to 300 degrees, lay a layer of aluminum foil in a baking pan and sprinkle 1/2 an envelope of Lipton Onion Soup on the foil; place a 3-5 lb chuck roast seasoned with fresh pepper on top and wrap tightly (very airtightly) like a package. Roast at 300 degrees for 4 hours and you will have a tender pot roast that will fill the house with aroma.
Delicious roast carrots alongside: peel 8-12 medium size carrots and toss with T. of olive oil, kosher salt and fresh pepper. Place in baking dish and cover with foil. Roast in oven for 50 minutes (just put the dish in with the pot roast about 50 minutes before you are ready to serve.)
Use the time you saved in the kitchen to impress your girlfriend's parents by: cleaning the bathroom and putting fresh flowers in there; serving some nice nuts and cheese with their favorite drink before dinner; making a simple green salad, and asking your girlfriend what their favorite dessert is and getting the best version at your favorite bakery. Don't forget to get good coffee too! Have fun and good luck--enjoy yourself and make them feel comfortable.
One correction to the Idiot's Delight pot roast above. Don't forget to sprinkle the remaining 1/2 of the dry onion soup mix over the top of the roast before you wrap it up!