hotels - anything in Center City will work. You could go into University City (cheaper) but not further west than 40th or so.
You do not want to rent a car unless you need to leave the city. Center City is incredibly walkable - it takes about 40 minutes to walk from one side to the other. Public transit is dicey...there are two subways (one north-south, one east-west) and a bunch of regional rails but seriously, you can walk almost everywhere in the downtown.
To get to PPL Park, you'll need a car. You can take the SEPTA to Chester, but the train station is about 2 miles from the stadium and Chester is...sketchy at best and I wouldn't walk around there at night. You could cab but it would be expensive. It wouldn't be a terrible idea to take the train to the airport, then grab a cab from there...it's only about 5 miles.
My favorite things to do:
- touristy stuff (Liberty Bell, Constitution Center, Mutter Museum, Art Museum, the Barnes is amazing)
- walk around. Philly has great places to walk. Lots of good people watching in the parks (Rittenhouse, Franklin Square, Schuykill River Park)
- eat and drink. Amazing bars and restaurants.