The History Department of your public library will have (or can get you) very good books about Lebanese and Syrian immigrants. Dr. Alixa Naff's "Becoming American: The Early Arab Immigrant Experience" (1985) is excellent, and should be read by anyone whose people came from Lebanon or Syria. Be sure to read Dr. Philip Hitti's "Syrians in America" (1924), and Lucius Hopkins Miller's "A Study of the Syrian Communities of Greater New York" (1904). If your library does not own them, you can probably obtain them through interlibrary loan. Although not recent, the latter two books have the advantage of being contemporary with the original immigrants. A very good resource book for researchers of non-European families is "The Family Historian's Handbook" by Yaffa Draznin. Tell your librarian what you are doing and ask for suggestions. He or she can guide you to other books and sources of information.
If you like to cook, or are interested in food history, two recently published books will be of interest to you. "Recipes and Remembrances from an Eastern Mediterranean Kitchen" by Sonia Uvezian is beautifully illustrated with lovely old pictures and drawings of Lebanon and Syria, in addition to stories and mouthwatering recipes. Also worth reading is "A Mediterranean Feast" by Clifford A. Wright, a well-researched history of Mediterranean countries, with recipes and culinary histories for each of them.
You may want to do a community history or a series of interviews -- an oral history -- as my brother and I did in St. Louis and Dr. Alixa Naff did on a national level.
An interesting result might be that others in the community will begin working on their family histories. Organize classes to teach children about their heritage, and help them begin their own family histories. Offer Arabic language classes at your church or community center. You will have other ideas for your own family and community. All these projects will result in a greater interest and pride in our legacy, and a greater appreciation for those ancestors whose courage enabled us to live in this Country of peace and freedom.
Finally, don't let your hard work go to waste. Give each of your children and other family members a copy of your family history. Give a copy to your public library and local history association, and if a church serving members of your community exists in your area, give them a copy as well. Be generous with the fruits of your labor - family and community histories are most valuable when they are shared.