Many favorite lcoal museums offer weekly free or discounts on certain days of the week. I wouldn't suggest that you always go on free day, but it can be a treat and an incentive to try a museum you've never been to before. A couple museums in the borough are free and definitely worth a visit.
You can always enjoy the sight of the rockets above the museum, and the farmers market that opened in 2009 can offer smells (at least) that are free; but there's nothing like Fridays 2-5 p.m. on Sundays 10-11 a.m. (all year except July and August) for free admission.
Admission to the famous Warm Up summertime parties is free if you can prove that you're a local resident of Long Island City. This deal is probably one of the best museum events of the year.
Otherwise, admission to P.S. 1 is free if have MoMA ticket from within 30 days.
Meg Cotner of JIA
The sculture rock garden at the Noguchi Museum is small, but mighty tranquil. Free your mind sitting in the garden on (almost) free admission day; that's the first Friday of every month when museum admission is pay what you wish.
The Queens County Farm Museum is free, but once you arrive, there may be fees for feeding the animals or joining hayrides or the like. The museum does charge for its many special events and for experiences like hay rides and the Amazing Maize Maze.
The Socrates Sculpture Park does not normally charge admission.Most days it is open for you to explore. Most of the special events held at Socrates are also free.
Admission is always free. The Fisher Landau is an underrated, off-the-rader, private art facility in the Dutch Kills area of Long Island City. If you make the trek, you'll be treated to nearly empty galleries showcasing some of the bigger names in contemporary art in the last 50 years.