humbolt park is probably not a good choice. logan square, wicker park, ukranian village, irving park, pilsen or west town are all good choices if you need to be close to downtown. they are all within riding distance of everything. you can find an apartment for pretty cheap but it wont be super nice. if you dont mind taking a train, pretty much anywhere is an option. the public transportation is really good and covers the city and most of the suburbs. as far as suburbs go, oak park is the nicest. also consider lincolnwood, north park, skokie, norwood, park ridge or jefferson park. they are all a 20-30 min train ride from downtown and are pretty good neighborhoods.
the art institute is a really good school. the museum is amazing.