Yay. Philadelphia is great --- if I weren't heading to NYU, I'd definitely stay around Philadelphia --- I love it here. Though I will be here on the weekends for the most part.
As for places to live, Northern Liberties and Old City are both nice; however, both of them are rather pricey for what you get. They are somewhat trendy and alas, the rent is high. Old City is rather loud on the weekends: it is the nightlife destination for lots of the city. But if you're up for a lot of bars and clubs and such, it's a nice place --- plus it's a pretty neighborhood. Northern Liberties lacks a supermarket, but as your husband will be commuting to Princeton, you'll have a car --- so that will probably not be much of an issue. Honestly, it depends on what type of neighborhood you're looking for.
You should really consider West Philadelphia--particularly University City/Powelton Village. I know some people who are in the same situation (Upenn for one, Princeton for the other) who live in Powelton. You will find the best rents, biggest apartments and most green space in those areas--apartments are often in old, beautiful victorian houses. While some places are touch-and-go, most everything west to 48th street and south of Chestnut (until Kingsessing Ave) is quite safe--that's a huge area--however, there are some great deals elsewhere. There are also pockets where tons of graduate students live (usually west of 43rd or so) --- it's quite a nice community. West Philly also has easy access to 76 which feeds right into 95 and the Vine Street (I-676) expressway. The traffic is far from ideal, but by living in West Philly, you'd save money and you'd be able to walk to class. Plus parking is easy. That said, my girlfriend and I don't live in West Philly but I work there and she goes to veterinary school at Penn. We live in an area called Fitler Square, to the southwest of Rittenhouse Square in Center City. It's a quiet residential neighborhood which has nice parks (namely an awesome dog park) and a supermarket, breakfast place, coffee shop, etc. within a block or two. Rents here are a bit more than W. Philly, but you can find deals (we did!) and we love it here. 10 minute walk to Rittenhouse, 15-20 minute walk to Upenn and 3 blocks from 76.
Other areas to consider would be Fishtown, directly to the northeast of Northern Liberties. You can get a house there for a rather reasonable rent --- and though some of it is a little bit gross looking, it's safe and there is a bunch of bars and restaurants that are springing up. It is right alongside I-95 and you can jump on the Blue Line L and be in University City within 15 minutes (we timed it when we were thinking about moving there). I wouldn't go further to the Northeast, though, as you soon hit Kensington and that gets a bit seedier.
I hope this helps! There are lots of choices: people who don't know Philly tend to give certain places bad reputations without looking at it. Around Penn is fine, as is large sections of the Northeast. Of course, Center City is also great --- but the neighborhoods I listed above usually have a fairly large residential component (with perhaps Old City being the exception).