Diet & Exercise Assistant lets you choose between having the app calculate it or doing it yourself, but it doesn't have all the entry points you're looking for. Just type, time, and calories.
I'm so glad to have a chance to promote one of my favorite apps: Pace. Look it up. It's just for running and walking (not weights, biking, etc.) but it does everything you want and more simply and elegantly. One of my favorite hidden gems of the app store. 🙂