The parkway closings are still in force, but never in July or August. So they start again Sunday 9/11 and continue through mid October.

However Westchester County, north of White Plains is a cyclist's playground with plenty of rolling 2 lane roads with light traffic, and drivers used to bicycles.

If you want cycle trails, there is still the mid county trail which follows a closed rail bed running almost 50 miles (with an interruption or two) all the way south to the NYC border. Also you can get a pass which allows you to take your bicycle on commuter trains except during rush hour peaks. Combining the 3 lines of rail service with Hudson River bridge crossings it opens up an area not quite as large as Texas, but plenty enough that you can ride 100 miles daily for weeks or months without exhausting all possibilities.

If you need more, post info about where you're thinking of staying and the length you're comfortable riding daily.