How often is a tire replaced on a 777?
Aircraft tires are replaced on condition, but maingear tires usually last about 250 cycles. A 777 in longhaul usage might only get two cycles a day, so a set of tires would last about four months. 

The 777 uses a 50x20.0r22 with 32ply rating. I couldn't find that exact tire but a similar one costs $4700 new. It is common practice to retread or remold worn tires after inspecting the carcass to ensure its serviceability, and these cost about half of new. 

Interestingly, this study by Embry-Riddle suggests that 99% of tire wear could be eliminated by prespinning the tires prior to touchdown, eliminating the puff of smoke you see as a part of the tire burns away as it matches up to relative runway speed. If correct, a tire would effectively last forever, until it was damaged as by debris or a hard landing.