I have been using Runkeeper Pro on my Droid X. I do use the GPS function, but you don't HAVE to use it. I travel a lot for work, and use the app to log workouts at hotels in addition to rides at home. There is a website that will allow you to track your progress, and for an annual subscription you can get reporting trends, too.
I've been pleased. It does not have a spot to record weather, but you can put in notes on your rides. And, you can archive your rides, too, so you can easily log them later.