I second the Priceline suggestion.
You can do one of those hop on/hop off trolley lines that take you around to all of the sites, or you can do Phlash, which is a purple bus that takes you around to the same places. I would look into each cost.
In the Old City area, you can find all of the historic stuff. Liberty Bell, Independence Hall, the Constitution Center, and that's where most of the tourist trolleys are based, so that's a good place to start. That is a good home base, and that's at 5th and Market Streets.
For 13 years old, I also think a trip to the Franklin Institute is cool, it's on the Benjamin Franklin Parkway at 20th street. It's a great place to explore some science stuff. Right next door is the Academy of Natural Sciences, which is also pretty cool. Dinosaur bones and stuff, also big into science as you can tell by the name. Most 13 year olds would love both of those too. I would look both up online to see if any cool exhibits are there while you're there.
The Art museum is at the end of the parkway, as is the Rodin museum, but unless your DD is really into art, I would save that for a later visit.
For fun, South Street is a fun place to go walk around at little shops. The folks who hang there range in age, but it's mostly teens and/or young adults. If you do go there, eat at Lorenzo's pizza at 3rd and South. (My fav) And if you want a cheesesteak, you can eat at Jims which is a block away. Though I think a trip to South Philly is in order for a Cheesesteak. Pats and Genos are around the corner from each other. If you have a car, from center city, take 10th street a few blocks past washington and you will see it on the left. I'm a Pat's gal, but you should get one from each and taste test for yourself. It's fun.
I also strongly suggest Reading Terminal Market. Go on a Saturday morning and eat breakfast at Jack's or at the counter at the Amish place. Saturday is more fun than Sunday because the Amish places are open, but it's more crowded too. It gets really bad between 12-2, that being said, it doesn't stop me from shopping there on Saturdays during that time period. (and until a year ago, I was pushing twins in a double stroller, so it can be done) Again, cool places to eat and shop. The Ice Cream shop there is awesome, and quite a few places there have been features on the Food Network over the years. (Jack's is owned by the guy who co-hosted Bobby Flay's first show on Food Network "Grillin and Chillin") There is no bad place there, but I have a few I highly recommend. Any amish place, Jack's (BBQ and Breakfast) and Hershel's (Jewish Deli - best Pastrami ever!!!!).
I know there are tourist tickets on sale at the Franklin Institute, Academy of Natural Sciences and at the Constitution center that has a book of discounted tickets at $60ish pp for a bunch of places, that's pretty cool. I will try and find out the name for you. Independence Hall is free, same for the Liberty Bell.
Normally I would say check out the Camden Aquarium, but the Baltimore one is cooler, so for you I wouldn't say it's worth it. She'll be too old for Please Touch museum. I'm not one to push the Betsy Ross Museum, because contrary to popular opinion, Betsy Ross didn't sew the first american flag, they're just a rich family to successfully re-wrote history, but I digress....
If you have any questions, let me know. I live not far from Old City and am in town every day shopping and eating and travelling. So I'm happy to help in any way.
