Fine lines under my eyes/on top of my cheek bones when my face is at rest. Options? (photos)

Under eye wrinkles can be permanently corrected with surgery or temporarily camouflaged with fillers (Restylane, Belotero, Volbella).There are great non-surgical options to fill in under eye depressions and hollowness. Using dermal fillers, a liquid eye-lift can be performed. A dermal filler such as Restylane would be placed in the cheek and tear trough to hide the depression or bag underneath your eye. 
Surgery would require a fat-repositioning lower lid blepharoplasty. In this surgical procedure, fat from the eye area is moved into the tear trough depression filling the actual depression. 
I hope this helps!

The under eye area is complicated and needs to be addressed in the 3 dimensions.  First, adding filler can help with any contour or volume deficits.  Second, treatment with Botox can help with dynamic lines and also improve the static lines.  Finally, skin resurfacing with laser, chemical peel or other energy technology can help smooth and strengthen the skin.  

From the photos provided, I would have to agree with you, i.e. that treating your cheeks appropriately with volumizing fillers would likely substantively improve your under eye concerns. This is supported by the fact that when you smile, these lines diminish--which is likely due to the fact that smiling raises up residual fat deposits that have migrated downward and temporarily repositions them in a more youthful location, and hence the temporary improvement in the lines. Although photos are no substitute for an in-person examination that allows for palpation and manipulation of the skin, it appears that  you would indeed profit from volumizing filler place in the cheekbone and to some extent in the mid-face region. In my NY office, my volumizer of choice for this purpose would be Voluma XC, whereas in my Israel satellite facility, where a far greater number of regulatory agency approved volumizers are available, I would opt for Stylage XXL. It is hard to say from the photos, but you might also benefit from a couple of microdroplets of Botox placed appropriately in the infraorbital region. You would be wise to seek consultation from a board certified aesthetic physician and exercise a heavy dose of skepticism when evaluating claims for this or that fraxel or other so-called energy-based devices, as the claims for these relatively expensive treatments are typically far more heavily supported by device manufacturer backed marketing hype than hard science. Ask to see his/her personal before and after photos before agreeing to proceed. Best of luck.