I program java every now and then as a hobby. I have made a simple game but I would like to add on to it and make it more complex and fun. Would asking for additional game elements or for a new direction to take my game on Programmers SE be on topic and appreciated?
Game design isn't something that is the realm of the conceptual or architectural software design. Questions about MVC, or organization of the code may be on topic here, but the game elements themselves would likely be off topic.
You may wish to look into GameDev.SE and asking in their chat room first about how to structure the question or even if its appropriate on the main site (often such questions can be answered in chat... though I'm not active on GameDev or their chat so can't say for sure).
You can drop by Code Review and get the code for your game review, if what you have is already working.
Be aware though that Code Review is not there to ask for "feature requests", but to clean up your code - which can make it possible for complex things to be added easier. (Although some people might come up with feature requests anyway...)