I had the opportunity to travel to Philadelphia on a horticultural odyssey this past March. The weather was unseasonably warm while I was there; the weather made it a great trip. I always wanted to attend the Philadelphia Flower Show. That was my first stop and I went there during the week thinking that it would be less crowded. It was mobbed. There were so many people that at certain locations in the convention center you couldn't move; you stood still until the crowd moved. I can't recommend it. After the Flower Show we went to Bartram's Garden. The Garden is historically significant as being, I think, the first botanical garden in America. The Garden was recommended by the National Geographic Guide to gardening, but I can't recommend this one either. While an interesting historical story, and there are some old, amazing trees still on the site, if you are short on time, I would pass this one up. I've posted a picture.
The next stop was Terrain at Styers, which is a relatively new retail garden/lifestyle concept store from Urban Outfitters. I think Terrain was launched 3-4 years ago and at the time it was launched the focus was on the plants. Over the intervening years, the concept for the store changed to a "gardening lifestyle" focus and away from the plants themselves. I'm guessing the plants are less profitable than the the furniture and accoutrements of gardening (organic towels, soaps and oils, dishes).
Finally, the highlight of the trip was Longwood Gardens. I would thoroughly recommend this one. There aren't many places that can be described as "grand," but Longwood fits the bill. A beautiful garden. Also, the conservatory is huge and has a wonderful plant selection. The blue Himalayan poppies were in bloom when I was there.
After Longwood, we visited Winterthur. Also, a recommended place from me. While the focus at Winterthur is more on the house than on the grounds, the grounds are lovely.