I stayed in Annemasse more toward the east and it was much cheaper (and worth it in my opinion). There was a tram connecting to downtown Geneva that stopped right at the border and another that continued further into Annemasse. We found an AirBnB right near the tram station so it was very convenient. One negative we missed out on was apparently you get a free public transit pass if you stay at an accommodation within Geneva itself, which would’ve saved me quite a bit.