Suggestions for making the most out of a set graduate school program?
For graduate programs with this kind of structure, there is usually an expectation that your core courses (algebra and analysis) will be your main focus for the first year.  So you should not necessarily expect to have much extra time to spend on other topics during that year, nor will the program be expecting you to do so.

If you find that you are able to handle those courses pretty easily and have a significant amount of extra time and energy, then you could consider:


studying additional topics on your own
enrolling in other courses, if there are some that don't have the core courses as prerequisite
approaching an individual professor in an area of your interest about a reading course or independent study


But if not then don't worry about it.  There will be plenty of time after your first year to explore other areas of math, and having a thorough grounding in core areas will make that exploration much more productive.