Stir-fry may be the easiest thing to cook.  Veggies sauteed in olive oil OR you can use a viniagrette tpe salad dressing which adds flavor and the oil at the same time so the veggies won't stick.  Don't use creamy dressings that won't work.  If you want to cut down on the fat put a splash of water in at a time after the veggies have started to cook in a couple table spoons of the oil or flavored dressing -- I call this 'steam-frying'.

You can put the veggies on top of or mix with cooked noodles (spaghetti or other long noodles, rice noodles, or your favorite pasta shape - really any will work) OR you can put the veggies on top of cooked rice. 

Some common veggie combinations might be choosing from this list: onions, bell peppers, zuchini, broccoli, pea pods, (the list can go on and on... - pick the ones you like).
You can also add firm or extra-firm tofu chunks, seitan (wheat gluten) or tempeh (cultured soy beans pressed into a rectangluar slice) or fake meat substitutes (such as fake chicken) but if you are not familiar with these you could just go with the veggies for your first cooking date. 
If you are nervuous about cooking for your date I would recommend using the simplest menu and the ingredients that you are most familiar with.  That is unless your date likes to cook, you could ask her to show you how to cook some unfamiliar ingredients. Your date will be impressed that you made the effort to make a veg meal. 
Good luck, and have fun!
Let us know how it went!
Delia
ecodel22 ;)