Stay downtown, really. I don't think it'll cost more if you go about it the right way. Have you considered using Hotwire to book your reservation? I'm more than happy to help identify hotels on their website.
I looked up your dates (the nights of 7/6 and 7/7) and here's what I found - 2 good options - I put in 2 adults and 1 child in the search criteria to ensure getting 2 beds:
4 star hotel in Historic District/Penn's Landing - the Hyatt Regency at Penn's Landing - $95/night - great hotel, nice indoor pool, great location (rgiht near historic district and Old City) - one of the best bargains in the city, in my opinion - we stayed there in April - it's right on the river with great views
3 star hotel in Center City East - I believe this one is the Crowne Plaza at 18th and Market, right in the middle of center city - I've stayed there before. It's a nice property with smaller rooms - rooftop outdoor pool - $64/night
I'm not sure what your budget it - but honestly, if I had to choose between these two hotels, I'd stay at the Hyatt.
I looked on Expedia and there is nothing that even comes close to these two prices.
I'm more than willing to help you try Priceline as well. Let me know and good luck!