Must go to Reading Terminal for breakfast or lunch. Lots of great places to eat. Some are Amish some are not.
Independence Hall is nearby with the liberty bell.
There are hop on/hop off buses that give you lots of history about Philly. Also Segway tours of old city. Did that with the wife, it was pretty cool.
Yea, skip Reading Terminal. I was born and raised in Philadelphia and honestly, it's overhyped. Not only is it overly (Read as: unbearably) crowded, it's full of many eateries that have received numerous health code violations, many of which are straight ignorance.
I live in Center City and many residents avoid the market at all costs; instead, we hit up local farmers markets to support local farms and businesses.
The only thing worth traveling to Reading Terminal Market for are the donuts by Beiler's (The Amish; note: they are off Sunday and Monday).
Check out uwishunu.com! They have a weekly post (Usually posted on Thursdays) about what's happening in and around the city.
Also, this week, it's Wine Week!!! Lot's of events going on. Check out http://phillywineweek.org/ for more info.
I live right by the Liberty Bell so maybe I am biased, but I'd say walk on Chestnut Street between 5th & 6th to take a peak. I mean, it is the Liberty Bell after all - haha!
What are you into? Local things? Touristy attractions? Dive Bars? Swanky Cocktail Lounges? I have quite a few recommendations!
If you enjoy a great cocktail and a swanky vibe, check out Hop Sing Laundromat (Cash only and you must be dressed appropriately: no sneakers, etc.).