Hi,
I will bet most of the restaurants in this thread on
Restaurants open Christmas Eve and Day will likely be open on New Year's Day.
For the price range you were discussing, Sun Wah BBQ on Argyle would keep you in your price range, exotic enough to keep you entertained, little your teens could complain about and definitely family friendly.
Wherever you do choose visit, call ahead to avoid any chance of disapointment. As always, have a plan B because a line out the door discourages me from visiting.
If you really want to try new stuff, there is
Afghan Kabob on Montrose just a few store fronts in from Elston.
If you do a search for 'family' for topic titles only for Eating in Chicagoland, then there are at least 14 threads to check out, with some information perhaps of use.
Regards,