How can I improve the area around my eyes?

Thank you for your question. I suggest that you move forward and consult with a board certified facial plastic surgeon because you seem to be a candidate for blepharoplasty and eyelid rejuvenation.
Best wishes,

If the negative canthal tilt shape of your eyes is what is bothering you, then it is possible to make eyes more almond shaped. It requires raising the lower lids and canthus. 

Interesting question.  I think your eyes and eyelid area look to be youthful, with good skin and a nice, well-positioned crease.  You mentioned two things for which I could offer suggestions—the first is the under eye bags, and the second is that you feel the eyes are “masculine.”  For the former issue, a fine hyaluronic acid filler (Restylane Silk) might be quite nice to smooth and soften the look of the lower eye region.  For the latter, I actually think that some eyebrow shaping may help.  A masculine brow sits at the brow bone, similar to yours, whereas a more feminine brow will sit slightly above and with more of an arch.

These are suggestions to fine tune your appearance because otherwise you are just fine :)