Where does computational chemistry overlap with organic chemistry?
The first thing that comes to mind: read the backlist of Henry Rzepa's and (especially) Steven Bachrach's blogs.  Depending exactly on what resources you have available, there are lots of things they do on the computational side of organic chemistry that you could at first imitate and then use as a springboard to innovate.

In particular, I've found Bachrach's posts on reaction dynamics to be especially fascinating.  This is the phenomenon where the topography of the potential energy surface near a transition state is such that the reactions don't always follow the minimum-energy path due, effectively, to the inertia of the nuclei as they cross the TS.

I also have a personal interest in Bader's Quantum Theory of Atoms in Molecules, which uses the topology of the electron density to divide molecules up into atoms, where each atomic volume is enclosed by a 'zero-flux surface' in the electron density.  (There's some ongoing controversy over the theory, but it makes good sense to me, for whatever that's worth.)  Bader's book is a good place to start; or, you can search the journal literature for Richard Bader and a whole bunch of examples will surely turn up. I engaged with Dr. Rzepa last year in the comment thread of a post of his about electrides that touched on QTAIM, the electron localization function (ELF), non-covalent interactions (NCI), etc.

Finally, I've been very curious lately about 'charge-shift bonding', a relatively newly described class of bond where the nuclear framework tries to cram so many electrons into a small space that in the end Pauli repulsion drives them apart, causing what might otherwise appear to be a covalent bond to instead take the form of a resonance between two ionic structures.  (The electronic structure of $\ce{F_2},$ for example, is better described as a balanced resonance between $\ce{F- \!- F+}$ and $\ce{F+ \!- F-}$ overlaid atop a very weak covalent interaction, than as a purely covalent $\ce{F\!-F}$ species.) Search the literature for Sason Shaik's work for more information and examples.

Other things that I've come across that have seemed interesting include carbenes, cyclic alkynes, unusual Diels-Alder reactions, and fullerene systems.

I would also subscribe to, e.g., Computational Chemistry Highlights, CCL, and Jan Jensen's Computational Chemistry Daily -- the posts and/or questions that come across there might give you some inspiration.