Sierra,
I literally just made this trip this past weekend heading east on the inside and returning home via the ocean. I draft 4'4" and air draft 18' with antennas down.
East Rockaway is the easiest inlet and the least amount of time spent in the ocean. However, taking that route, you will encounter 6 bridges and no wake zones. On this route, the first bridge is Atlantic Beach. You should make it under without an opening with no problem as it is high enough. If you are concerned, the outer spans are 33 ft. From here, you pretty much need the rest opened. The Leeds RR bridge is low and most boats need it opened. Immediately following is the Long Beach Road Bridges which I think are 21-25ft closed. Next you will detour around to the north to the Loop Parkway bridge (the fixed bridge is too low). Again the bascule is about a 21ft clearance closed. Next will be the Meadowbrook Parkway bridge, again about 21ft. Last the Wantagh Parkway Bridge (sloop channel?) which is only 18ft closed. At 24 ft you will likely require openings at three to four of the five. I believe the bridges for the Loop, Meadowbrook and Wantagh are manned by a lone tender who drives between them so you may be waiting for him. Once you have passed the last bridge you stick to the channel and endure a few 5mph zones. I went north through the Babylon Cut (Oak Island Channel) and found good water to the North Channel. I was careful about staying center in the channels and had no low water issues.
Your alternative is to run the ocean to Fire Island Inlet. Despite what has been written and the LNM, I found good water all the way through at mid-tide. However, due to the narrow nature and sharp turn around Democrat Point, this would seem to be nasty on a rough day. Assuming a calm day, once inside I believe you can come around and under the Captree Bridge and use the state channel to get back to the Babylon or Lindenhurst Cuts or a straight shot farther east to the West Channel which is wide and has plenty of water. There are several guys from the Anchorage who can speak to the water around Lindenhurst and the conditions of the channels around the Captree bridge. I believe it has more clearance but I don't have latest information as I've never gone that way.
IMO. On a rough day East Rockaway is the best inlet. Jones is narrow but will get you past 3 of the bridges you will likely need opened (leaving 2). Fire Island may get you there without any openings and few if any no wake zones.
It's a mixed bag. Hope this is helpful.