There are many and varied media sources available for characters to use. Here's a short and ready list of suggestions:
The Daily Bugle (NYC)
The Daily Planet (Metropolis)
The Daily Globe (NYC, rival to the Bugle, run by Barney Buskin)
Gotham Gazette (Gotham)
Starling City Star (Starling)
Weekly World Enquiry (Basically the Inquirer)
Gotham Globe (has a hard-on for villains, especially crazy ones, does lots of interviews like "Penguin Forgives Parents" and "Joker: Madman or Genius")
Just The Facts w. J. Jonah Jameson -- angry and incoherent conspiracy theories promoted around New York, mostly focusing on Spider-Man.
TV News Stations
ENN -- Essential News Network. National News, HQ in NYC, generally a fair news source
ENN Headline News -- ENN's every 15 minute fast news network, running 24-hours
WAC -- Weather and Climate. Basically the Weather channel. Has occasional disaster porn shows.
LXINN -- "Lixin", LexCorp International News Network. GENERALLY a fair new source, though occasionally does turn anti-alien. A subsidiary of LexCorp
OENN -- One Earth News Network, heavy anti-meta but especially anti-mutant bias
KNN -- Keystone News Network, based in Metropolis, also heavy anti-meta bias, really hates Flash for some reason
GBS -- Globe Broadcasting System, has some top notch investigators but big pull is notorious meta-critic G. Gordon Godfrey.
New York and surrounding:
Channel 6 News: News You Can Count On
WJBP-TV Channel 8: Here. Now. Happening.
Metropolis and Surrounding:
GBC Gotham Broadcasting Channel 7: Reliable. Factual. News.
Starling City and Surrounding:
KSF-TV Channel 4: The Star of Starling