I've tried a bunch and have settled back on The Weather Channel. I even bought the ad-free version. It isn't the prettiest, but it has the best information, at least for where I am. It includes radar, which is important in tornado country.
I have CurrentTemp for the badge with the present temperature, which is pushed on an hourly basis.
Weather Bug Elite lurks on a back page, not quite consigned to oblivion, but I haven't used it in a long time.
I also have WeatherAlert, which just pushes notice of weather alerts - I guess that's what its name says. So I have three apps, one for push for current temperature, one for push of weather alerts, and one for the forecast and radar. If I could get that all in one application, I'd be really interested in that!