I want to use my car stereo to play music in the garage without killing the battery, can I simply use a battery tender (
such as this one)? Or would there be issues I'm not aware of?
Battery tender will help but it depends on how loud and for how long you play it. Big ass stereos with 1000(s) of watts pull massive current relative to lower powered ones.
You'll need to monitor your voltage levels on the battery while the car is off and the stereo is playing. Without the tender on.
If you are talking about just playing it at normal in car listening levels for less than an hour at a time, your tender solution should work. I'd just be weary of your battery dying sooner than one would expect.
Best way to go would be to get an AGM / gel cell battery designed to take the beating of having its voltage dropped low and often. Mating that with a smart charger with intelligence built in to charge and not over charge the battery will extend the life of the battery.