hi shilpa,
if you are planning a day trip from NJ, do start very early in the day...
we made a hasty,last minute planned trip last weekend and got caught in the trafffic...we lost close to a couple of hours because of that and could'nt see much...
the bes place to park would be the East Potomac Park, as this is close to the Tidal Basin...you might have to search for a spot further inside the Park if you reach there late in the day, but there are free shuttle buses that drop you in front of the tidal basin...
you can take a walk around the tidal basin, take a peek at jefferson memorial, washington monument, capitol etc... and then visit some museums...DC has lots of them, so since you are planning just for a day, you can plan to choose just one or two you like...
it was bright but very windy last week, so check the weather and take your jackets, etc accordingly...
do chk the previous discussion on this here -
cherry blossom festival to see if its useful to you...