Place recommendations don't tend to take the weather into account. You don't really want to visit the park when it's pouring outside, do you? AccuWeather certainly doesn't think so -- it's partnering with Foursquare on a "hyper-local" recommendation system in MinuteCast that takes the conditions into account when pointing you to new destinations. It'll suggest the beach or the pool on a hot day, or point you to a nearby coffee shop if you want shelter from the rain.
And yes, AccuWeather is aware of privacy concerns. You'll have to opt-in to sharing you location, and this can be turned off. Foursquare's place data also strips out personally identifying info.
Of course, there is a financial incentive for AccuWeather to do this: ad money. The move will let in-app advertisers target users based on where they tend to go. If you're often at the gym, a restaurant might pitch you on its healthy options. That might put you off the recommendation system if you're hesitant to allow any kind of ad targeting (no matter how anonymous). However, AccuWeather is clearly betting that you're willing to make that tradeoff if it keeps you cool or dry.