In Starfield, you can equip both a spacesuit and helmet, and a set of civilian attire—but the weird thing is, by default your space gear is always what's visible, no matter where you are. If you want to know how to hide your spacesuit in Starfield, read on.
First step is to open up the character menu and click on the Inventory in the bottom right. Navigate to your equipped spacesuit, and you should see an option that says "Hide spacesuit in settlements". Press the T key, or RB if you're using a gamepad, to enable this option, and the game will then automatically hide your spacesuit whenever you're in a city or anywhere else of a civilised nature, revealing your fashionable duds beneath.
It's a bit odd that this option isn't enabled by default, considering how immersion-breaking it is to be hanging out at the Lodge for the first time looking like Neil Armstrong while everyone else is in their casualwear, but at least once you've found it and switched it on you don't need to think about it again. The only thing that will still show in cities is your boost pack—if you jump and boost while in a settlement, the pack will appear, and stay on your back until your boost recharges. It's a magic boost pack, don't worry about it.
If you're sitting there wondering "How do I even see myself in the first place?", you may have missed the "Toggle POV" key. By default, it's set to the middle mouse button, or the select button on gamepad, and it allows you to switch between first-person view, third-person view, and a more zoomed-out third-person view—perfect for gazing lovingly at the space explorer you spent two hours in the character creator perfecting.