What next?

I've finished singe variable calculus and I want a taste of pure mathematics before I go to university next September. I'm going to get a grasp of sets and proof first but what next? Number theory, analysis or what? Book recommendations would be ideal!

Elementary differential equations are not exciting by any means. They are useful, and the advanced stuff can get really fun, but they should not be used in a survey of higher math. Algebra is LOTS of fun - check out "Contemporary Abstract Algebra" by Gallian - its only prerequisite is a tiny amount of set theory and familiarity with the concept of a function. There's an elementary book on topology by Michael Henle (the title of which escapes me) which you might like.