I'm having trouble with my left/right hand coordination. I'll either fret the wrong string, or pick the wrong string. I'm trying not to look down at the guitar because I know it's a bad habit, but this is frustrating because I keep missing notes. Do I just need to be patient and let muscle memory kick in? Or are there any exercises or tips to help coordinate the two hands so they're landing on the right places?
You can absolutely look at the strings and frets until you build up the muscle memory and then learn to play without looking. I can't imagine trying to learn guitar without looking ever.
Professional guitarists look. It's good to learn to play without looking, but it's not something that should be 100% avoided from day one.
Keep your picking hand close or touching the bridge, behind it. That will give you some stability. You can practise playing different strings, open if you like, by sliding across a little.
Your eyes need to be looking at the frets/strings/fingers. At the beginning, they are so important - your eyes, I mean! When you finish a note, try not to wave your fingers about too high above the fretboard. Move gently, as most of the time, you'll only be moving the the next string, either way.
The more playing you do, the more time you'll have to watch those listening to you, which is also quite important !!
Practice, practice and more practice. Then practice some more. When you see the pros they are looking to make sure they're at the right fret, not the right string. Your fingers get used to feeling the adjacent strings until you don't even think about being on the right one anymore. But where you are on the neck is tough to get a feel for.
Oh and ... go practice some more. Keep it fun so you WANT to practice!
Use speed as the self-indicator to your performance.
Play slowly enough to play perfectly, even if this means playing one note every three seconds. Increase speed as your confidence with the technique increases.
One of my favorite ways to reinforce a riff that I know is to play it faster and faster to sharpen the muscle memory.