Swift seems pretty good....just tried it this morning and it's now my default client. Tweetdroid has lots of features, but the interface isn't very finger friendly.
i like twidroid actually, if you google "best twitter app for android" you'll find a site, and a guy has a good review of all of them and there's even a grid-layout checklist on which ones have certain features
for time and weather, i use Beautiful Widgets (not free, but i think it's done very well) it is a SenseUI type design. for twitter, Twidgit Lite was one i used before moving to Swift, and while fairly basic, it did all i needed a twitter widget to do.