I have one published biography (of someone who left a large volume of correspondence) and am working on the research for a second one (of someone whose papers did not survive). I know how difficult it can be to find the type of information that you will need.
Having worked extensively on intelligence gathering during the Gettysburg Campaign, I am very familiar with George Sharpe. The following suggestions are presented in no particular order and are offered in the hope that you find some useful suggestions here from someone who has walked more than a mile in this particular pair of moccasins.
First, and foremost, obtain Sharpe's service records from the NARA. RG 94.
Then, obtain the pension records, if there are any.
Since Sharpe was the head of the Bureau of Military Information, you will need to visit NARA to see what's in their records. Before doing so, you will want to read Ed Fishel's really outstanding book,
The Secret War for the Union. Fishel was the one who discovered those records, and nobody knew them like he did.
You will want to review the regimental books and records, particularly for the 120th NY. Those are also in NARA. You will also find some excellent research resources here:
http://dmna.ny.gov/historic/reghist/civil/infantry/120thInf/120thInfMain.htm, including a couple of items penned by Sharpe himself.
New York State Adjutant General records will be useful, and regimental colonels had to file regular reports with their state AGO's.
Due to Sharpe's role as regimental colonel and then head of the BMI, there is quite a bit of correspondence to and from him in the Official Records. You will want to obtain each and every one of those items.
Since Sharpe was a lawyer, you will want to review whatever records are available through the New York State Bar Association. You will probably find some useful records in the county where he lived.
Local historical societies in the county where Sharpe resided can be very useful. There may even be items of his there.
Join a newspaper database such as newspapers.com and spend a lot of time combing through those records. Newspapers are some of my favorite sources. Obituaries are usually tremendous sources of good and useful information. Since you know the date and place of his death--New York City--be sure to search the free on-line archives of the New York Times and find his obituary. Be sure to spend ample time on the National Tribune, which was a veterans' weekly newspaper. The Trib has traditionally been underutilized, but it's one of my favorite sources.
Sharpe may have joined the Military Order of the Loyal Legion of the United States (MOLLUS). In order to join MOLLUS, you had to have been a Union officer. Whenever a MOLLUS member died, an obituary pamphlet was published. Those can be valuable sources of information.
Genealogy will provide you with good information. Look for a published family genealogy. Once you find that, you will be able to piece together the puzzle of who the family was.
When all else fails, back fill in from other sources.
Expect this to be a long and frustrating process. In the absence of a treasure trove of material by your subject, it will come in fits and starts, and you will get frustrated. Take your time--this search will take time--and don't quit until you feel like you've turned over every rock that might yield useful information. Good luck.