I'm entering my senior and planning to apply for grad school. It kinda baffles me where I should apply, so I'm hoping to get some advise. Really appreciate it. Here's my profile:

Undergrad institution: UCLA

Major: Pure math

Upper div math GPA: 3.93 (will boost up a little to 3.95 if I get A's this coming fall)

Undergrad courses taken by graduation (some are already done and some are in plan, but definitely will take): Linear Algrbra, Real & Complex Analysis, Abstract Algebra, Differential Geometry, System of Differential Equation, ODE, PDE, Probability Theory, Topology, and Combinatorics.

GRE: Not taken yet, General will be early Nov, Sub in Oct.

Program Applying: Pure math

Research Experience: N/A

Awards/Honors: Dean's Honor list for 2 out of 3 quarters in UCLA (transferred from community college in 2012). Actually, got A's in both upper div math classes last quarter, but registered for less than 12 units so cannot be in that damn list.....

Activities or Jobs: Tutored for a year, and hopefully HW grader this coming academic year.

Any Miscellaneous Points that Might Help: Will consult the Dept to try to get in a grad course. Will try to get a recommendation letter from Dept Vice Chair, who happened to be one of my professors. Other two letters will probably come from less famous and relatively young faculties, but are strong anyway.

Given my profile above, I'm shooting to stay at UCLA for grad school, but have no idea how much of a chance to get in. Other schools, I'm not sure yet, but NYU looks to be also a goal. Other than that, I don't know what caliber of schools to apply for.

Any reply or suggestion would be helpful and appreciated.