It's extremely difficult for me to enjoy most 8-bit games, as there's very little there to intrigue my tastes. However, there are a few standouts that I still play to this day on an emulator handheld, like H.E.R.O. or Mr. Do!
The good ones generally have a really solid little gameplay loop that's quick to get into, with tight controls that let you get into a flow-state easily, and a difficulty curve that isn't infuriating (something far too common from that era). The story heavy games from that era usually had mediocre or terrible writing paired with repetitive grinding gameplay, so the classics like Final Fantasy are sadly off limits for me.
H.E.R.O. is one of my favorites since it has somewhat uncommon gameplay where you control a man with a helicopter pack in a mine, avoiding various hazards to rescue a trapped miner at the end of each level. It rewards memorization, which is a knock against it, but even though I've played it heavily, I keep coming back to it as I never can quite remember the layouts of the later levels, and once control of the backpack is mastered, it just feels good to zip around all of these creatures and caverns of instant death without nicking yourself. I'm not sure how someone who has never played it before would feel about it, since it can take a while to get the hang of the controls, but I think it holds up pretty well from that era.
It also received a pretty massive number of ports to various consoles and home computers. The original Atari 2600 version is good, but personally I found the MSX port to be the most polished, and it adds some nice additional graphics as well.