Not many Filipino restaurants in Chicago, I have dined at a few which I wrote up threads for, I'll have to try and find them.

From the book The Food Lover's Atlas of the World which I received a few years ago while participating in the FT Secret Santa, it states the following for the Phillipines:

Signature dishes:
Lumpia - Filipino version of egg roll
Adobo - dish usually containing chicken, beef or pork, marinated and cooked in seasoned palm vinegar. Some consider adobo the national dish
Asado - meat simmered in soy sauce with onion, tomato, peppercorns, bayleaves
Tamals - banana leaf or corn husk packages filled with rice, coconut milk, ground peanuts, meat, achiote
Lechon - crispy skinned roast suckling pig sometimes served with a sauce made from the liver

Like other Southeast Asians, use of dried fish and fermented fish sauces and pastes to flavor dishes. Rice based cuisine but noodles are important. South Pacific influences here such as yams, taro. Of course Spanish influences such as chorizo, jicama and chocolate.

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