You can do some research by googling the model number and seeing if anybody's made any comments on the matter, but it's a fairly universal problem with HDTVs and it's not just the HDMI input but everything it's feeding in.
Some TVs will have a "gaming" setting that will turn off most of the post processing stuff to decrease the delay but they're almost never 100%. If they have a computer VGA or DVI port, they may use less post processing on those inputs than the others as well.
Having your system output at the TV's native resolution will also help, but this isn't always possible. Retro systems have no such settings, and many TV's actual native resolution isn't "standard" Most "720p" TVs, for example, are built with screens that are actually 1366x768 instead of 1280x720. 720p signal has to be resized up, adding delay. 1080i or p signal has to be resized down, adding delay.
Most modern games have enough give in their input timing that none of this is a big issue. Because the developers are well aware of it being a thing. Retro games that are expecting the nigh-instantaneousness of a CRT setup aren't as forgiving. And certain genres suffer even in modern games, namely the more timing-intensive stuff like tourney-level fighting games or rhythm games.
And that last note gives us our best way to really test how much delay your TV is adding... Rock Band 2 (and up). You see, to compensate for you TV's delay, Rockband is designed to counter-delay the video and audio. In the first game they had you play along to some visual and audio indicators (lights and metronome) to adjust the timing, and that's still an option in later games if you're using the original guitars. But starting with RB2, the upgraded guitars came with some built in microphones so the guitar can listen to the metronome on the TV and the game can adjust more precisely. The TV will add as much delay to the audio as it does to the video so that everything stays in sync, so the delay that Rock Band 2 detects between when it outputs the sound and when the guitar hears it is precise.
