SEPTA transportation’s generally pretty good if you’re you coming from the suburbs to center city and vice versa. (If you’re trying to go from suburb to suburb that aren’t on a direct line -like you want to circle the city - you’re in trouble). There are 3 main train terminals in Center City - Market East, Suburban and 30th St. Most of the regional lines (R-#) stop at multiples. There’s also a (smallish) subway system to get you around parts of Philly. As a whole though, most commuter trains are pretty full in my experience.
If you’re trying to get from Philly to South Jersey, you take the PATCO line, which is a different company than SEPTA (which runs the regional lines, the subway, etc). The PATCO line doesn’t come into the main 3 terminals, but a few blocks away … and I think the Market East stop is connected underground, but it’s been a while.
Some areas that are a little further away that might be worth looking at:
Conshohocken - it’s just outside Philadelphia proper, so you actually get to avoid paying city wage tax and since its a suburb, its a little more spread out, meaning have a car and traveling isn’t so bad. As a bonus, it’s also really close to King of Prussia (maybe 10 mins by car) which has a huge number of corporations if you need to look for a new job ever, as well as the King of Prussia Mall - one of the largest on the east coast.
Conshy (as the locals likes to call it) has 2 SEPTA stops, sits right on the river and is undergoing gentrification. It’s becoming a hot town to live in for the 20-30 crowd with a small, but growing downtown. It’s also convenient to get to Manayunk, which is about 10 years further down the same gentrification path.
Manayunk / Roxborough - was mentioned further up. It’s a great town to be in if you’re in your 20s/30s and like the “hipper” life. Lots of pubs, bars and restaurants downtown along the river, which could be easy to get to (or not, it’s a VERY steep-hilly area). It’s also part of Philadelphia, so wage tax comes into play.
In that area, I’d avoid most of the Northeast. Parts are very nice, parts are very much not. Without seeing in person and being sure of the exact location, it’s probably good to stay away from.
If you’re looking to cross the river, which would be my suggestion (being a Jersey boy), look into these areas:
Cherry Hill - great commuter town, actually named after one of the larger and older indoor malls in the region. There’s a few sections of town that may not be so great, but for the most part it’s solidly middle class.
Maple Shade - has a great “main street”. If you can get within a few blocks of main street, you get a quaint little town feel.
Moorestown - probably the best you can get in the area. Schools are consistently ranked very high and the downtown main street is pretty cute.
Haddonfield / Haddon Heights - these two areas are great suburbs and closer to the PATCO train line into Philly. Haddonfield in particular has a great little downtown with a bunch of small shops and little cafes and restaurants.
Other areas of South Jersey around Philly are pretty good too, as long as you avoid Camden, most of Pennsauken … actually most of the river towns. This is a generalization, but most were built during the industrial boom and what you would think has great land value cause it’s on the river, really doesn’t.
All that said - if you’re going to live outside of center city Philly proper, you’re going to need a car (or two). South Jersey and South Eastern Pennsylvania require driving to get to most places. Even the downtowns I talk about aren’t huge. They’re cute, they’re worth a stroll and living in one means you can probably do dinner or something a couple nights a week without having to drive, but outside of that…
Good luck!
I probably wouldn’t recognize it now, though, since I think major renovations had just started when I graduated ('93).