There are a few options walking distance from IHP. If you are a vegetarian, here are some suggestions

• C'midi on rue Saint Jacques is a pleasant salad bar, kind of expensive but you get to create your own salad.
• Kokonor on rue Saint Jacques (just after C'midi) has a lunch menu with several vegetarian options.
• Pasta e fagioli on rue Claude Bernard, so a 5 minutes walk from IHP. Great pizza, approved by a native italian! Gets full very quickly, so you don't find a place to sit, the trattoria I Diavoletti on the other side of the street is a great option too.
• Pizzeria Luciana on rue Saint Jacques is very close to IHP. The food is average but the management is niche and they have a room on the first floor to accomodate bigger groups.
• Au Vieux Cèdre on rue Saint Jacques is very close to IHP has good falafels, hummus and other vegetarian options and is cheap but has no good seating options.

You can also have a look at La Fourchette (The Fork) website where you can search by location, type of cuisine, etc: http://www.thefork.com/city/paris/415144 and check out the IHP recommendations from their website.