Congrats on your journey. I would start by heading down to Bar Harbor, Maine.
From there, if you want to see NYC, Washington, etc., I would recommend you use the ACA Atlantic Coast route. Since the east coast is so densely populated, finding a decent route is a chore and they have done the work for you. Once in Washington, you can take the W&OD rail trail out toward the Skyline Drive/Blue Ridge Parkway (if you do not mind climbs). This will eventually intersect with the TransAm near Roanoke, Virginia. Or you can stay on the Atlantic Coast route until it intersects the TransAm in Fredericksburg, VA.
If you want to bypass the east coast, you could head over on the Northern Tier route through scenic New Hampshire and Vermont and angle down to Niagara Falls where you could pick up the Underground Railroad route. This route heads southwest and bisects the TransAm in Kentucky. This would save you some time as it is less miles plus less "big city" stops for sightseeing.
If you are a member of ACA, you can download all the GPS waypoints so you do not HAVE to buy the maps but they are really good maps. If you buy the maps, it probably makes sense to join as it is not too expensive. However, they do not show where to wild camp. I would think after 4 years though you would be an expert on that
The USA is really weak on hostels. They are mainly on the east and west coast with a few scattered elsewhere. They are definitely more of bonus than the usual type of accommodation. You are much better off with using WarmShowers as there are a LOT more of those than hostels. As you get into the center part of the country, many small towns along the TransAm will allow cyclists to pitch their tent for free. Once you get west of into the Colorado (or points west), there is a lot of public land (Forest Service, Bureau of Land Management (BLM), etc. which you can legally camp on usually.
Finally, check out CrazyGuyonaBike.com for a ton of journals and such. Very good site for the touring cyclist.
Best wishes, John