Never got to play this as a kid, but I wanted to finally get it off my pile of shame. Trying it without a guide, but I can't shake the feeling that I'm constantly missing heart pieces. Everytime the game tells me to go somewhere I feel like I should be searching the entire map looking for these things. Any advice on this or any other tips?

There aren't any missable items in Link to the Past, so don't stress over it too much. Maybe jot down the ones you do get in case you decide to go back over with a guide for the ones you missed. But the game's totally beatable without all of them for a first timer, just stock up on potions or faeries if you're having trouble. Most heart pieces are gated by requiring a certain item to get anyway.

My tip is not to worry about the heart pieces and just enjoy the game. You'll get enough from boss victories.

Awesome, I think I'll take all that advice and just play the game. I wasn't sure how critical they were.