Dave, welcome to the forum. To start with your last two questions first ( those are the easy ones! ). To check if there is a stamp club in Binghamton NY please go to the following website:
http://stamps.org . It is the website of the largest American stamp club, the American Philatelic Society. You do not have to be a member to access information from them. On their homepage go to the first box ( stamp collecting ) and look for local clubs. Just fill in your ZIP code and / or state name and you will get a list of all the clubs in your area! And if you contact the club they can tell you about places to trade, most likely the club meeting will be one of them!
The removal of old hinges is a bit of a tricky thing. If the previous owner used a quality hinge it will not be any trouble; like you said they will more or less just fall off. If they do not fall off or come off easy, don't try to force it. If part of the paper comes with the hinge the stamp is worthless! The best thing to do with these is either steam or just soaking. If the stamp is mint I would recommend steaming, if used usually soaking is the best way!
And good luck to you and your daughter! Years ago when my little girl was still little she collected stamps until she discovered boys. That took care of it!
Peter