Someone already posted MOMA, seeing your location it was the first thing I thought of and it is free on Fridays. If you have a student id then a lot of the museums will give you a discount. I also suggest going to MoMA PS1 in Long Island City, Five Points a famous graffiti spot is right near it and it will be torn down shortly so those are two cool things to see next to each other. The Met and Museum of Natural History are also great. You should check out the Highline, a park over the Meat Packing district, with great views and an interesting concept. There are a lot of galleries in SoHo that let you browse, try walking the blocks from Houston south to Broome, between Greene and Lafayette. You haven't mentioned what music you like or would be interested in, I can offer a lot of suggestions based on what you like and there are a lot of good free cheap things. There are a lot of Spanish food options so it depends on what you are looking for if you want guidance
Some cheap eats I like-
Patisserie Claude for chocolate croissants and quiche($2-4 per item) is really just awesome 187 W 4th St
Biryani Cart for their chicken kati rolls(46th and 6th)
Dessert Truck for their hot chocolate(check twitter and they have a location)
Prosperity Dumpling for dumplings and their off the menu duck scallion pancake about $5 for a whole meal(Eldridge St)
Mexican truck(forgot the name) for chicken or cheese with pepper tamales $2 each(4th Ave at Astor Pl weekdays)
Aroma for really good Israeli coffee and burekas sandwich- pastry with potato, egg, hummus, pickle $6(Houston and Greene)
check
Real Cheap Eats NYC - 194 Cheap Eats for $10 or Less in New York for good ideas too
Khyber Pass is a lot of fun and close to Mc Sorleys, the second oldest bar in NY. You should also check shops like Trash and Vaudeville while you are on St Marks
Your profile says you are Native American and if you are into your culture, the National Museum of the Native American is in the financial district
National Museum of the American Indian
The cheaper and better comedy clubs are West Village, sometimes no cover if you go early but there is usually a drink minimum
A few things I recommend-
- get a one week unlimited Metro Card
- take the bus instead of the subway if you are heading downtown so you can get off if you see something that interests you
- avoid comedy club scams around Times Sq
- map out what you want to do on a subway map before you get here
- to Brooklyn at least once and Queens for Spanish food