The most common problem with onions is gas, and it's worse when the onions are raw. Nevertheless, if she's sensitive to onions it would display more sensitivity on your part not to inquire too deeply into the private digestive affairs of a stranger since there are so many good alternatives.
Spaghetti without onion isn't a problem. Many white sauces are made without onion or garlic either. There are the many variations of al burro, including the classice Alfredo. Carabonara is a delicious choice, and like Alfredo, is fun to make tableside. If garlic isn't an issue you could make a nice, white clam sauce.
And if you must go red, there's puttanesca -- one of my favorites -- which may be made quite well without onion although it does need garlic (not to mention olives and anchovies). Similarly a very satisfying arrabiata may be made without onions -- if she can handle the garlic and pepper. With both of these there's enough going on that you won't miss the onions much.
There are alternatives to noodles. How about a risotto with a saute of early spring vegetables.
You don't need garlic on the bread either. Olive bread is good, and there are a number of Italian style breads with sesame crusts which will speak to the Greek in you. They don't need anything more than a dip in good olive oil; and they're quite nice dry if served with a dressed salad and pasta.
Unless you're going nuts on the olive oil for the pasta course, go with a true Caesar salad. You just can't beat it for an informal-friends dinner. I posted a great recipe for Caesar on CT quite awhile ago. If you can't find it with a search, I'll repost.
One of the great things about a simple dinner like the one you're planning is the opportunity to enjoy a nice wine. Frascati anyone?