newport is a very nice safe place and it is close to NYC (only 10min path train to world trade center, and 20min to 33rd St). Newport is a subregion of Jersey city, NJ. You should be able to get a 3 star hotel in Newport for around $70 per night by bidding on priceline.

Secaucus NJ in north bergen is also safe and close to NYC. Around 25min by bus to port authority in 42nd St of manhattan.

It will take you at least 50min from flushing to 42nd street. The pro about flushing is it has a lot of chinese restaurants.