This portion of the river comprises everything from the the public boat launch located off of PA state route 65 in New Brighton to Kelly's Riverside Saloon..
First some comments about the map bearings. The boat launch is at the northern edge of the map. The bottom half of the map is the Fallston side of the river. The top half of the map is the New Brighton side of the river.
1. Just downstream of the boat launch there is a stream that empties into the river. At the mouth of the stream is a large shallow point that drops off to a depth of 10 feet. This point is good for either casting or trolling to catch bass and sauger. Sometimes the fish will be in very shallow water so cast as close to shore as you can with shallow diving crankbaits.
2. The main river channel from the New Brighton boat launch to Kelly's Riverside saloon offers plenty of trolling opportunities to catch bass, sauger, catfish, and walleye. Water depth ranges from 10' - 14'. I would recommend using CD6 Wally Divers or Storm Hot'N Tots with orange, chartreuse, or chrome coloration.
In summer troll at 2-3 mph. When the water is cooler troll at 1-2 mph.
3. Downstream of the boat launch on the Fallston side the shoreline is heavily wooded with many overhanging and submerged trees. This shoreline is good for catching bass and sauger by casting or trolling. Water depth along the shore is 6'-8' so CD5 Wally Divers and Cordell Big O's are good for trolling.
4. At the mouth of Brady's Run creek there is a large shallow underwater point that will hold bass, sauger, and walleyes. Sometimes these fish will be in shallow water feeding on shad and minnows. Look for the small fish jumping at the surface of the water near shore. At other times the fish will be stationed in deeper water. There is a ledge along the point that drops from 6'-7' to a depth of 8'. Casting or trolling will work to catch these fish.
5. Downstream of Brady's run creek there are two bridge piers that remain from a demolished bridge. The pier nearest the Fallston side of the river sits on a shallow flat that is 4' - 6' deep. Trolling this flat with Cordell Big O's or CD5 Wally Divers on a short line can be produce bass and the occasional sauger from time to time. There is also a 8' hole adjacent to the pier that occasionally holds fish.
6. The other bridge pier, on the New Brighton side of the river demarks the transition from the shallow flat to the main river channel which is 11' - 13'. This transition has a distinct ledge where the flat drops off to deep water. Trolling or casting along this ledge can produce bass, sauger, and walleye. The largest walleye (24"/ 5+ pounds)that I have caught in the Beaver river was taken with a CD5 Wally Diver trolled at 8' along the ledge.
7.Next to Kelly's Riverside Saloon there is a small stream that empties into the river along the Fallston side. There is a small point at the stream mouth that drops into 6'-8' depths. Sometimes this points holds bass, which can be caught by casting shallow running crankbaits. The creek and point are not real obvious from the middle of the river as they are between two marinas, one used and the other disused. You can't miss Kelly's however, as it is the only place on the river with palm trees and reggae music.