Sounds like you're headed for nonfiction? In addition to the other great ideas, try your local small-town newspaper. (If you live in the city, there's usually a big daily but there are still smaller, sometimes local papers as well.) And try the local newsletter for seniors, and the one from the hospital that goes out to all the doctors, and the one for the arts scene . . . whatever you can find. In a smallish operation (5 staff members or less), the editor is almost guarranteed to welcome an appropriate article idea. Steer clear of "hard" news (usually the domain of the journalist) and do features. That would include things like "Eating healthy at the Farmer's Market," an article that talks about how much fresher the produce is and quotes research suggesting fresher food is better for you. Or a profile of a local hero, a business that overcame great odds, a review of the best places to jog . . . .
For local papers, keep your ideas business-friendly. The local businesses are the paper's advertisers and basically give the editor her/his job, so anything celebrating business is usually welcome.
And here's a freebee: editors devour side bars. You know, those boxes next to the article with complimentary content. Look at some newspaper features and any magazine and you'll spot them. Even if your editors do not always use them, the fact you provide them will impress.
Also, if you've got a decent camera and know how to use it, offer some photos to accompany the feature.
Come with a couple clear ideas and why they are timely and interesting for the readership. Just ask for permission to write and submit the feature, with the understanding that if it turns out that you can't write worth beans, it doesn't run. Pay careful attention to what the editor tells you s/he needs and whatever you do, don't act like the finished piece is sent from above and unworthy of the red editor's pen -- that's the ultimate mark of a difficult freelancer and not someone the editor will want to work with in the future.
The smallest town papers (10,000 circulation or less) will not pay, but if you stick around and keep submitting pieces, you'll build up a portfolio you can take to a bigger player. Newspaper work looks great to magazine editors because it implies you can succeed under tight deadlines. Also, once you prove your ability and reliability, eventually newspapers will start sending you to more fun events like charity benefits, etc. You can get clips for your portfolio and free food!
If you stick around long enough, maybe you can eventually ask the editor for more "career" advice. If the editor likes you, s/he is likely to have contacts at bigger (better paying) papers or magazines s/he might share.
I was a freelance writer and journalist for 5 years before my current incarnation as a mama . . . it can be a lot of fun to be connected and feel informed about the community, whether that is through a narrowly focused newsletter or a town paper. Just find a way to get out there!