Well imo if you didn't have children I would say Center City, but since you do have children I would recommend living along the Main-line area-Villanova-Haverford-Bryn Mawr-Narberth where they have beautiful homes, terrific schools and almost zero crime. Center City,not all of Philadelphia, just Center City(Rittenhouse-Soceity HIll-Queens Village-Bella Vista--Old City) has a very nice quality of life to it. Downtown Philly imo other than Boston probably resembles the narrow streets and quaintness of the European cities the most, but the downfall is that a couple a miles away things kind of fall apart signifigantly. Great place to visit. Great place to live if you are young, single, or retired but unfortunately its not the greatest place for families. Although I do see more and more baby strollers in and around Center City.
I would give a strong recommendation for the Main-line towns and to Chestnut Hill which is a spectacular section of northwest Philadelphia. Very quaint, very unique, very well designed.
Other possibilities if you are looking for a more open suburban feel such as rolling hills and valleys are towns like West Chester, Swarthmore,New Hope, Valley Forge area and Doylestown.
$2000- $3000 dollars gives you some pretty decent housing options. Here is a good site that will give an idea of some of the housing prices in the area. There are 4 counties(Montgomery, Bucks, Delaware, Chester) that surround Philadelphia and they are all great places to live.
There is a search feature for rental houses allows you to puch in your rent range and county you wish to move to. The mainline towns border Montgomery and Delaware Counties.
Give a looksee to Chestnut Hill, Villanova,Narberth,Haverford and Gladwyne if you decide to come this way.
Good luck.
http://www.weichertrents.com/search/....aspx?state=PA