Stayed at 10 Deux Ponts myself for several years.....Second Le Pre Verre - best deal around and lively and fun spot. Had a nice gigot d'agneau for 14 € at Cafe Restaurant Louis Philippe, (just across Pont Louis Philippe) 66, Quai de l'Hôtel de Ville, 4th. The Brasserie is an institution and worth a stop, if only for a beer at the agreeable bar. Probably items on the menu that will work for your budget. Le Saint Regis across the street is decent, cheap, and reliable for simple stuff (Croques, salade, etc.) Fou de Lille on Deux Ponts was not bad either, and cheap. Avoid the Auberge de Deux Ponts. Awful. Lots of other cheap places on the Ile, but I haven't tried them. Bon voyage et bon appetite.
One of my favorite restaurants is just steps from there, and way under budget (well, I guess it depends how much you drink). La Reserve de Quasimodo is a cave a vins on the Ile de la Cite just across the bridge at Hotel de Ville (the Pont d'Arcole). They serve excellent tartines (foie gras and apple; potato, st nectaire cheese, and magret; etc), salads, cooked dishes, and a meat-and-wine fondu. You can pick your wine from their cave and the mark-up (droit de bouchon) is only 6 euro. It's an incredible deal and a really fun place. Very old building. Bathrooms are cool too.
With wine & coffee or just food?
Le Pre Verre
8 rue Thenard, 5th (Metro: Cluny La Sorbonne)
Closed Sunday and Monday lunch
Lunch menu 13 €, dinner 26 €.
3, rue des Grands-Degres, 5th (Metro : St Michel, Maubert-Mutualite)
T : 01.44.07.04.24
Lunch menu 13.50 €, dinner a la carte 40-60 €.