Moma has free friday nights 4-8 every week too. the trees are starting to bloom in central park if you do decide to go to the MET you can take a walk there as well. on park ave around 60th there is an art installation of these giant metal flowers, i last saw it a few weeks ago so im not sure if it is still there, you can probably google it.
the rock is my work backyard so i love watching the ice skaters, you can go to the concourse and there are tables that are NOT at the restaurants you can sit at on the rink level and watch the skaters without having to pay for a meal. they just put out the spring plants and put water back in the fountains at the rock too. i like exploring the concourse too but some of the buildings and part of the concourse are closed on the weekends. also close by is st.patrick's, if you happen to be catholic you can sit in on mass, if not you can just stop in and marvel at the beautiful architecture. window shopping on fifth is always fun too.
last weekend i took my mum down to chinatown, little italy, and soho. we spent $11 at babycakes and i bought a laundry bag and she got hair clips. other than that we spent no money while wandering around and had a great time.