Please run something! Help populate L.I. with good quizbowl as opposed to the RQB stuff. Anyways, to answer some of your questions with my opinions:
The cost should depend on your funding situation and the general price in the region, as well as how many rounds you offer. I'd say to look back at what LIFT cost, or HHHW cost and go from there, see if those fees will provide enough to cover your expenses for rooms, breakfast etc. You probably should offer similar discounts for buzzers and staff, as that's become pretty much standard.
As far as NAQT vs. housewrite, I'd advise to not try writing an entire tournament if you don't have significant writing experience, as I doubt the tournament would have a good reception, and teams probably wouldn't come back the next year. If you contribute to and mirror a different housewrite, that should alleviate some of the problems as there should be experienced editors overseeing the project.
You're probably fine with any date, as there are enough tournaments outside L.I. that teams would attend. I'd love it if you hold it during my Spring break so I could come staff, but that's personal preference, so don't think too much of it. Just make sure it's not on an SAT date and not too close to AP exams.
As far as scorekeeping stuffs, you can use the scoresheets on NAQT's website for any format, and then put them in with SQBS, found free at http://ai.stanford.edu/~csewell/sqbs/
. This has become pretty much the standard for scoresheet entry. Please keep individual statistics and bonus conversion, as these are very useful for comparisons across the country, and extremely simple to generate with SQBS. There's also an online stat entry program that someone here at UCLA wrote so you can input the stats from multiple computers. I can ask him about it if you want, or you can explore it at http://quizbowl.gimranov.com/
Hope this helps, and I hope I can get out to this next spring!