Putting in order my two packages and possibly merging them
The ideal package structure is one which indicates usage. Classes such as these which exclusively contain static methods are definitely utility classes, which I usually put in a util subpackage of your main application.

From what it sounds like, you don't have a main package at the moment which ideally would be your website (in reverse domain order), e.g. com.stackexchange.codereview so that the more specific elements are later, then on top of that you'd have the name of your application which may make it something like com.stackexchange.codereview.tweettrends.

This would be the core of your program, and from here you could then add on your extras.

The Twitter package in particular doesn't sound helpful: your entire program seems to relate to Twitter so it doesn't really convey what that part of the program does. Frankly, I'd just put all those classes under com.stackexchange.codereview.tweettrends.util and add in more sub-packages if you add more classes.

And generally speaking, in Java packages should be exclusively lowercase.