Dpends on what you're interested in. The commuter rail system (in SEPTA-ese the RRD, for Regional Rail Division) serves a number of areas inside the city plus a lot of suburban territory. The R1 runs from the airport to Center City (3 main stations). From there you can transfer to the other R-numbered lines (but see below). You can find maps on the SEPTA website
http://www.septa.org/service/rr_schedules.html.
My own thoughts about interesting lines -
The R5 is the longest line and runs from Paoli or Thorndale in the far western suburbs to Doylestown or Lansdale in the north. You get to see a lot of both new-money and old-money homes on the Paoli side, which uses the Amtrak/PRR Main Line.
One arm of the R7 serves Chestnut Hill, one of the more posh neighborhoods inside Philly while the other end heads up to Trenton. You can see a lot inside the city as opposed to the R5 which is mostly suburban.
The R2 runs all the way to Wilmington and Newark in Delaware (note that the Delaware town is pronounced new-ARK while the one in New Jersey is NEW-ark, or even "noork".
I'd recommend against the R6 Norristown, partly 'cause I had to ride it so many years and partly 'cause it goes through some pretty grotty areas; e.g. it passes by the Norristown sewage treatment facility. Not too bad in winter but overwhelming in summer.
Don't ask why there is no R4. It's a looonnggg story....
The kicker is going to be fares. SEPTA is one of the most expensive systems in the country and most payment options are geared to regular commuters. Most single fares are between Center City and an outside station. However if you're taking a trip that goes through Center City with only a transfer at one of the 3 stations (i.e. no stopover) you can buy a ticket from one side of the system to the other for only a bit more than a one-sided fare. Just keep your ticket for proof of payment when (or if) you change trains.
There is a Day Pass but IIRC its use is limited to a single ride on the RRD.
The other option if you're doing a LOT of travelling would be to buy a weekly pass for the maximum zone number you plan to visit. That'll give you unlimited rides, but it may not be cost-effective. You'll have to look at the fares on the website and decide.
Enjoy!