When is your trip? Are you in AC now? It looks like we have fair weather and flat seas for at least the early part of this week.
Depending on how much time you want to take, the prettiest anchorages, hands down, are Barnegat Light (called Myers Hole), and Sandy Hook Point. If you want to take the time, I would spend a night at each and make 3 very easy days to cover the distance.
Barnegat will fall well short of it's nasty reputation right about now. The channel markers start well outside of the inlet and are very easy to find on a clear day. There is no need to start in at the outer pair (I see them marked "1" and "2" on navionics. I usually cut into the channel at markers "3" and "4" and head straight for the northern half of the opening between the jetties. The ends of the jettyies have fixed day markers "7" (green) on the south jetty wall and "6" (red) on the north wall.
Tide is high in the afternoon for the next several days, so the north jetty will be submerged when you approach. DO NOT pass #6 with the marker and the jetty on your port side! You will be on the rocks. You will see a lot of small skiffs fishing in that area. I don't see #5 on Navionics but I suppose it is in the middle between the jetty ends. Sailboats always stay to the north half of the opening. You will easily find the channel markers as you are passing through the inlet. It looks like currents are flooding in the later afternoons this week. Outgoing current is 3 knots so you will want to avoid max ebb currents that will be closer to noon. Slack currents between ebb and flood does not coincide with high tide. Slack current occurs about 3 hours earlier than high tide, so it is best to ride in at the end of a rising tide, which will be late afternoon this week. You can sleep in before leaving AC.
Within the channel inside markers #3 & #4 it gets shallow and you will see small breaking waves surrounding the channel and even inside the channel. If you stay within the marked channel, you will see depths get shallow to just under 10'. Locals typically round the channel entirely to the north side and only veer into the inlet right next to the end of the north jetty wall (which will be underwater - but the day marker is clearly standing out). Navionics shows the deep water very clearly when navigating around the north side of the marked channel. You may see boats heading toward the beach north of the wall and wonder why they are steering to the north of the channel, until you see them cutting inside just outside the end of the north jetty.
Once inside, Myers Hole anchorage is just between the Barnegat Light and the High Bar Peninsula. You'll find boats anchored there and within that area are some private moorings. A few weekends ago, our club had 14 boats anchored in Myers Hole, so there should be plenty of room when you are there.
Manasquan Inlet is more centrally located if you want to make just one overnight. I've never been in there so I don't have anything to say about it, except that I think you won't find an anchorage inside the inlet. You can stay at a marina, but you may have to navigate 2 bridges once you are inside. The inlet is easy and straightforward. I've heard that the marinas are very nice, expensive, and rolly because there will be a steady stream of sport fishing boats going both directions at all hours. (Barnegat has a commercial fleet of large fishing boats and party fishing boats that can also be a source of noise and waves throughout the night - but I think they are considerably more considerate!)
Sandy Hook point is a good anchorage just inside the end of the peninsula! It's just outside a coast guard station at Fort Hancock and the Sea Streak ferry service may come through there, but I think mostly on weekends. There is no need to go all the way inside to the Highlands anchorage. It is secure and protected just inside the point - as long as wind isn't from northwest. It should be fine this week!
