Hi Battiste,
I obtained my South African PPL and arrived in the USA about a week ago, also with the intention to build around 80 hours.
Planes are much cheaper here than they are in South Africa (and Belgium, I presume).
So far my research has indicated the cheapest places (more than one) to hire-and-fly a C150 or C152 (at around US$80 p/h, wet) to be near Wichita, Kansas (this is of course only from my own limited experience and better deals may be had elsewhere). It costs a good additional $350+ to travel to Wichita from NY.
Weilke and BillTIZ's advice is spot-on. If you already hold a PPL, you will first need the license validated by the FAA. This means contacting an FAA FSDO and completing the requisite form which can be obtained from the following link:
http://www.faa.gov/licenses_certificates/airmen_certification/foreign_license_verification/
The FAA recommends 60 days for this process. You will need to fax the completed form with your license and medical to the FAA, who will forward it to a designated official in your home country for confirmation of the validity of your license. As soon as your country has confirmed the validity of your license, you will receive a 'letter of authenticity' from the FAA which will allow you to approach the nominated USA FSDO on your form, in person, for your foreign PPL license to be validated and FAA license to be issued. I am told, once you have the requisite 'letter of authenticy', that the USA FSDO can theoretically issue your validated FAA license in as short a time as 30minutes - when you visit that FSDO in person.
The FAA and our local CAA in South Africa have been extremely helpful in my case. I arrived in Wichita, KS, on 17 May 2012 and applied for the 'letter of authenticity' the same day. The FAA sent the request to my home country on 21 May 2012 and our local SA CAA has responded to the FAA early this morning (23 May 2012). I was told that the FAA subsequently hopes to fax the 'letter of authenticity' to my nominated facsimile number in about five working days. Thereafter it is a simple matter to approach the designated FSDO FAA on your form (in my case this FSDO will be in Wichita) and to follow the 30 minute process of having the foreign license validated. All-in-all a very efficient process.
You will of course require a VISA (or not if your country participates in the Visa Waiver Program). TSA clearance is not required if you are only going to build hours - at least that was what I was told by the TSA.
The hassles aren't that many and I am sure all the planning and time spent travelling will be worth it, especially if you have a look at this post:
http://www.avcom.co.za/phpBB3/viewtopic.php?f=1&t=95591&p=1075132&hilit=flying+in+the+usa#p1075132
Let me know if you intend to visit Wichita and I'll hook you up with the most affordable and convenient places to stay, bus schedules, FBO's in the vicinity, etc.. Be aware that public transport availability and costs do vary markedly from city to city.
Best of luck and pleasant flying!