I live in the Philadelphia area, and when my family wants to do a quick get-away to just relax, we camp in Lancaster. BUT, where we camp in the area depends on several factors. Are there just two of you? Do you want a nice campground, very clean but without a pool, and yet central to the attractions in Lancaster? Then I would say, stay at Beacon Hill or Old Mill Stream. You really can't miss with either of these campgrounds.
I will also agree with previous posters, several campgrounds are shutting down in October, and because it is the end of the season, many campgrounds that are open do get rather full, so make reservations early.
And, do you have a tow? If so, driving to the train and going into Philadelphia is the way to go. Just make sure you know what connections to make. And, know when the last train leaves for the day, so you don't get stuck in the city. I wouldn't want to put you off taking the train and then the subway, but if you aren't public transportation people ( I say this because I'm not) then you have to know what you're doing. To my knowledge, there are no campgrounds very close to Philadelphia.
And, I would say, be aware that it can get cold in Pennsylvania in October. When we camp in October, I bring a heater along.
I would also mention that Lancaster has tons of stuff to do. You could easily spend a week just exploring the Lancaster area.
Best wishes on your vacation.