One of the blogs I read just did a huge series of posts about Twitter clients:
Part 1Part 2Part 3Part 4I hope one of the apps they recommend works for you. I'm an extremely light Twitter user, so the official app works great for me.
I'm not certain if there's a weather app as elegant as the one you describe (elegance is something that's only slowly coming to Android...very slowly

), but at the moment my favorite weather app is probably "The Weather Channel." Naturally, it's from The Weather Channel.
Sadly, I don't know what to recommend when it comes to clocks. I use the one that comes with Android because it pops up when I put my phone in its dock.