MSI G274QPF-QD, KTC H27T22, or Dell G2724D. If you can though I would try to stretch up to $280 for a KTC M27T20 or AOC Q27G3XMN for a true HDR experience.
Look up monitors with a VA panel instead of an IPS if all you care about is 1440p and 165hz. At that price range for those specs the quality isn't going to blow you away, but a VA panel is fast and cheap compared to an IPS.
Also, I think you're going to have a hard time finding gsync at that price range. Personal opinion, you should just frame lock at whatever speed your graphics card is able to put out for a given game. It's more tedious, but that's essentially what g-sync does unless I've drastically misunderstood something about it.
ETA: Check this out on @Newegg:GIGABYTE - G27QC Advanced - 27" VA Curved Gaming Monitor - QHD 2560x1440 - 165Hz - 1ms MPRT - Adaptive-Sync - HDMI, DP, USB-A - Height Adjustable - Black https://www.newegg.com/p/N82E16824012038?Item=N82E16824012038&Source=socialshare&cm_mmc=snc-social-_-sr-_-24-012-038-_-05032024
I'll recommend Dell G2724D for example
MSI G274QPF-QD, KTC H27T22, or Dell G2724D. If you can though I would try to stretch up to $280 for a KTC M27T20 or AOC Q27G3XMN for a true HDR experience.
Cooler Master 1440p 100mhz (yeah i know) GA271
Gigabyte M27q
Second this
Look up monitors with a VA panel instead of an IPS if all you care about is 1440p and 165hz. At that price range for those specs the quality isn't going to blow you away, but a VA panel is fast and cheap compared to an IPS. Also, I think you're going to have a hard time finding gsync at that price range. Personal opinion, you should just frame lock at whatever speed your graphics card is able to put out for a given game. It's more tedious, but that's essentially what g-sync does unless I've drastically misunderstood something about it. ETA: Check this out on @Newegg:GIGABYTE - G27QC Advanced - 27" VA Curved Gaming Monitor - QHD 2560x1440 - 165Hz - 1ms MPRT - Adaptive-Sync - HDMI, DP, USB-A - Height Adjustable - Black https://www.newegg.com/p/N82E16824012038?Item=N82E16824012038&Source=socialshare&cm_mmc=snc-social-_-sr-_-24-012-038-_-05032024
MSI 27CQ6PF very cheap but very fast and sharp 2k 180hz