That really depends on the specific brand of "theoretical and combinatorial aspects of computational geometry" you're most interested in. Any mathematical background has a strong potential to pay off in future research. Moreover, the best topics to study to master existing research is not necessarily the same as the best topics to study to generate new research.
To Suresh's excellent list, I would add linear algebra, combinatorics, graph theory, convex geometry, non-Euclidean geometry, differential topology, probability, statistics, optimization, logic, abstract algebra, category theory, randomized algorithms, approximation algorithms, online algorithms, data structures, and computational complexity. And a little computer graphics, animation, robotics, learning, vision, scientific computing, scheduling, VLSI design, compiler optimization, databases, distributed computing, ad hoc networking, sensor networking, game theory, signal processing, cartography, and graphic design wouldn't hurt, either.
Or to put it more simply: Everything.
Obviously you can't actually learn everything, unless you're Terry Tao. Where you should focus first depends on your specific strengths and interests. If you have a specific topic in mind, it's probably best to jump straight into some recent research papers and work your way backward to the specific background you need. (Got a nail? Look for hammers.) Conversely, if there's a particular area of mathematics you find appealing, study that area deeply and work your way forward to research applications. (Got a hammer? Look for nails.) Or best of all, work from both ends.
So... what do you like?