I think you would like Williamsburg. It's across the river from the East Village and some call it an extension of that.
It's home to a lot of artists, photographers, students and young professionals, particularly those in creative jobs or who just like being around creative types. It has a mix of converted loft buildings, new fancy loft buildings, gorgeous brownstones and tacky aluminum siding 3-flat row houses. A few great book stores, one that has great art, design & fashion stuff. Lots of up and coming art galleries, some call it "the new Chelsea." Also some young designer shops & studios. Mix of clubs, low key bars, trendy spots, old Italian and Polish restaurants that have been their since before the hipsters moved. There is a park, which is not the best in NYC, but it is full in the summer.
Really easy access to Manhattan on the L train, particular the parts you will want to go to (a straight shot to chelsea, meat packing district, east village). This is one of the most reliable, efficient subway lines. Look for something on one of the first 3 stops of the L train (bedford/ metropolitan/ graham) - perfectly safe. The 4th & 5th stops and further out are called East Williamsburg. They are a little less populated, warehousey with some very cool lofts for less money. It is getting better out there, but a not as safe for a single girl...
The new young, hip Williamsburg is mixed in with an old school Italian neighborhood, Dominican & Puerto Rican neighborhood, and Hassidic Jewish neighborhood. Borders on Greenpoint, which you might also want to look at, which is a an old Polish neighborhood. The downside of Greenpoint is the train service isn't as great.
You could check out this website to get a feel for the vibe: http://www.freewilliamsburg.com
I would definitely not waste your money or go into debt by living in Manhattan. You'll get a little break from "the city" while still being just as connected.