Family dinner near the Kimmel
We like the Happy Rooster, but it is small, dark and very casual. I can't see it as a birthday place.
Ted's would be more festive.
There is an Italian restaurant nearby that many people like - Ernesto's 1521 Cafe on Spruce Street. It is not BYOB, but close and pleasant. How are the girls in the better restaurants? This one is moderately priced.
A very good BYOB is Branzino, on 17th St. just north of Spruce. This is one of our favorites, attractive, very good food. But it is not quick, and I don't know how much your girls would enjoy it.
Also, be sure to check on what's open at 5pm. Some places don't open until 5:30 or 6.
There are several nice restaurants close by that aren't BYOB. You can have a good dinner across the street at Sotto Varalli and there are quite a few places north on Broad Street. You don't tend to see many children at these places with liquor licenses, but maybe someone else will have more suggestions.
If the girls are good "sitters", then Branzino would be very lovely. It's not terribly slow - just not fast.
Right across the street (Spruce St.) from the Kimmel Center is Ted's Montana Grill. We go there for the hamburgers (and sometimes I get their filet, which isn't bad) but I see they have a children's menu:
The service is very pleasant and it it quick - most children don't want to wait a long time for their food.
This isn't a gourmet place, but it is quite popular and should work out well for you.
There are several Italian BYOB's nearby, also, that would probably be okay but would mean a longer "sitting" time.