Cutting off cable service meant -- and still means -- losing local channels. And that means no local news. Unless...
If you have a TV antenna, you can watch TV that way. Just hook it up to your TV and watch. It's that simple.
Now, if you have multiple TVs, and want to watch local channels via antenna on more than just one TV, then you have a couple of options. One is to run antenna leads to the TVs you want. Another is to use a networking device that has a TV tuner, such as (for all major platforms) Tablo, Air TV, or (for Fire TV only) Fire TV Recast. Then, you just use your Roku, Apple TV, Google/Android TV, or Fire TV to watch local channels from your antenna.
If a TV antenna isn't possible, or isn't feasible, then you'll want to find a streaming solution. One is a live streaming service such as Hulu+Live TV ($65/month), YouTube TV ($65/month), Fubo ($65), and DirecTV Stream ($70/month), which carry all four major network stations,:ABC, CBS, Fox, and NBC. Vidgo ($55/month) carries local ABC, and Paramount+ ($10/month) carries local CBS.
All of those services get you more than just local TV, so you may find one a better selection than another.
For CBS, you do have the $10/month plan from Paramount+, which skips commercials from on-demand content, as well as getting you a live feed of your local CBS station.
For ABC, Fox, and NBC, you have to subscribe to a more expensive live streaming service. ABC can be viewed with Vidgo ($55/month), while ABC, Fox, and NBC can be viewed with Hulu+Live TV ($65), YouTube TV ($65), Fubo ($65), and DirecTV Stream ($70).
If it's just local news you want, there are some free options that might work for you.
NewsON carries clips from local news stations. It will try to automatically detect your location and present you with options from where it thinks you are. It will let you edit that, so if it gets it wrong, you'll still be okay.
Haystack News is another option for local news clips. I found that it didn't have as many local options for me as NewsON, but it still offered local content. The app also has many news categories apart from local news, if you are interested in that.
Local Now is more focused on local weather, but does have some local news mixed in. Local Now also has some on-demand ad-supported movies and TV, giving it a distinct difference from the other apps mentioned.
And, finally, you may find that your local news station has an app. Search your device for the specific local station, or look at the local station's Website and see if an app is listed there.
If you've been missing local news and weather from your Streaming Life, you have options. Perhaps one will fill the bill for you.