What is the best way to fix the old looking skin under my eyes? Fraxel laser? Filler in the tear trough, Surgery, cheek filler?

 Now is the perfect time to begin stimulating your skin to stay young with Fraxel Re:Store. It's a nonablative laser that can remove fine lines and wrinkles, plus stimulate your skin to begin producing more collagen and elastin, which will thicken and strengthen the skin plus make it more elastic. You will probably need at least two to three sessions. There is no downtime. Fraxel requires a yearly maintenance session as well. The Fraxel will also help thicken your eye skin and make it easier to resolve your tear troughs with a dermal filler such as Belotero or Restylane. Be sure to consult a board-certified dermatologist who has experience smoothing tear troughs with dermal fillers.

Your skin doesn't look particularly thin in the photos. Nevertheless, it can be stimulated to rejuvenate by using a variety of procedures, such as laser treatment with PicoWay, regular chemical peels, and a good, medical-grade skincare system, plus regular sun protection. As for your tear troughs, Belotero or Restylane dermal fillers can give you more volume and fill out the wrinkles. A board-certified dermatologist will be able to make recommendations for specific therapies during an in-person consultation and evaluation of your skin and tear troughs.

I would recommend a soft flexible filler for the tear troughs.  A lower bleph is an option, but filler will work nicely and you avoid surgery.  I would recommend Restylane Refyne or Volbella.  A laser resurfacing is always helpful to smooth and blend the skin.
Best of luck
Dr Rodman