Nightstand
Is there's weather app for the iPad that will always display the current weather without having to open it up?
Yeah, you could try Nightstand. We use it. It has a pretty good alarm clock. We use it on trips. Plus, it has the option of showing you your local weather. We use a data carrier chip but it should work from WIFI also. Cannot remember the cost if any. If you try it, click on the small I for information, click on weather, turn it on. It gives city, date (day and month), temp., high and low expected temperatures, a cute little icon and a not. Today, for us, it is "showers in the vicinity".
And, Czevski is correct. The Weather Channel is pretty good and just recently, if available in your area, you can set up your postal code and it gives weather for your vicinity for about Half a mile.
Hope this helps.