I'm from Newburyport and whenever I tire of Joppa I go to the southern tip of PI where there's plenty of room.
The Salisbury Jetty is also, IMO, more productive than any spot around. About 3/4 of the way out, on the beach side is a reef which is reliable at the top of the outgoing or on an incoming tide, don't risk going to the end of the jetty, it isn't worth it.
If you are fairly adventurous there's also Moseley Pines on the left hand side of Merrimac street just before you cross the Chain Bridge into Salisbury. It's a tough place to fly fish and a steep walk down to the river but a very productive place with a drift of a sinking line, especially with bait around. Big stripers hang in the flow. The island off of Chain Bridge is good too but it can get crowded with too many meat fisherman.
Off of Route 1 in Newbury near Fernald's are some good access points. Smelly marshes but it can be productive. The area is great with a canoe or kayak. I'm not sure if Fernald's still rents them though.
Also, Juro is right on with recommending the beachfront on PI. Everyone packs in at the point for the easy pickings and it's too popular. There are plenty of spots to park and decent beach access along the way. Some serious water moves along that beachfront and so do big stripers this time of year.