Go to Arch St & N Independence Mall E. See B. Frankie's grave, Christ Church. Walk south down Independence to Chestnut. See the Bell, Independence Hall. Walk east to S 3rd St, seeing the Second Bank, Carpenters Hall, First Bank. Walk south on 3rd to Walnut, see Merchant Exchange Building. Walk West on Walnut, see 18th Century Garden, Dolly Todd House. At Washington Square, walk diagonally down to Locust Street, keep walking west down Locust about 12 blocks to Rittenhouse Square, but stop along the way for lunch and a cocktail. Walk counter-clockwise around Rittenhouse and then go South on South 19th St, until South St. Head east on South St for 18 blocks, until 2nd St. Head North on 2nd St to Spruce St, and then head East for 2 blocks to Spruce Street Harbor. At this point it should be evening, and either you can go home or check out bars/restaurants in Old Town which is about where you are.
You can also take a detour at Broad St up to City Hall (take the Broad Street line subway up and back down if you're tired). See the hall, see the Masonic Temple, see the smallest "LOVE" sign ever at Love Park. Back towards Old City there's Thomas Jefferson's little place while he was writing it, Declaration House. There's the oldest continuously inhabited street in America, with a little art walk on Fridays around there. And of course there's the Art Museum and Waterworks behind it.
If you want to speed up your whole trip, make strategic use of Philly's Indego bikes. A bike is a great way to tour up the Schyulkill, to get to the Art Museum, and head north along the bike trail past boathouse row.