if you're planning to do boston too without a car...you can take the fung wah bus
https://www.fungwahbus.com/Default.aspx from NYC to Boston....really cheap at USD15 per 1-way (but please note luggage restriction if you aren't traveling light). it's quite convenient and the bus departs every hour. takes you about 4hours to reach boston chinatown from NYC.
it's quite a madness to drive in NYC and Boston but not impossible. last time we got around the 2 cities with just a paper map. these days we rely on GPS....still can be quite crazy (i.e. GPS signals might be lost in the tunnels, turnpike exits can be confusing, road conditions change etc.) but much easier than paper maps i'd say! for GPS....get one with lane guidance...very useful for city driving!
parking is much harder than in small cities/suburbs...so you'll need to plan in advance where to park, research for cheap parking garages (there are some discount coupons that you might be able to print online for better rates), some garages are cheap but require advanced online booking to get in. there are free roadside parking in NYC and Boston but you'll need to know the rules of parking...and usually, hard like hell to find free lots!! if it's still snowing in march then even more chaotic....'cos the curbside parking rules might change as need to shovel.
but driving can be fun la....especially in USA. if you are driving...you can do a triangular drive from NYC to Buffalo (niagara falls) through upstate NY (finger lakes region) and then across to boston and then back to NYC via the coastal route (through rhode island/connecticut etc). but not sure if you've sufficient time to do that though in 15days. NYC is nice...if you are into museums/theatres/musicals/galleries....you can easily spend a good 1-2weeks there without feeling bored. so all depends on how you like to travel.
one problem with new england travel is that the weather can be hard to predict. so you can plan your itinerary to a T...and then the weather changes and you'll have to re-plan again. so don't try to pack too much....otherwise you might be disappointed when you get lousy weather. always have some indoor options available for bad weather scenarios. we do still get snow in march sometimes even april. always watch the weather channel for updates so that you aren't caught off guard. and always be prepared (another reason why driving is good too then you can throw all your thick sweaters/mittens/hats in the back seat/boot just in case).
if you are driving....please arm yourself with LOADS and LOADS of quarters for the parking meters.
if you are a big shopper....the outlet malls here will drive you crazy. be prepared to spend a full day at one outlet. also, before you head out for shopping....always check online for any shopping coupons that you can print. sometimes, you can find coupons for outlet shopping i.e. coach etc. so you might be able to enjoy further 10-25% off the already low outlet prices. be aware that there are buying quotas at some of the branded bag boutiques i.e. LV, coach etc. so always ask first before you start filling up your shopping bag/cart.
have fun!!
side note: i'll be doing a roadtrip myself from southern MA to miami (& back) after xmas....if you are considering to visit washington DC etc...i shld be able to update you with more info after my trip. wish me luck and wish me good weather!