Spatial systems are usually boards made of spaces or squares, that players move pieces around. However, there are many degrees of spatial systems.
A spatial system is actually a repeated pattern of relationships between all the spaces on the board. This creates enormous intricacy in the game, but it's also easy to understand, as players easily understand which spaces are adjacent. This means spatial systems have an extraordinary Depth:Complexity ratio.
Chess, Go, and Scrabble are games that players can spend a lifetime playing. It's no coincidence that they all have a spatial system.
Many designers (myself included) instinctively try to represent our theme as it is in the real world — a spatial environment.
However, spatial systems have profound consequences for a game. This includes a plethora of hidden downsides. I've fallen into many of the traps created by using a spatial system, that I simply didn't understand at the time.
You should ask yourself if your game could possibly work without a spatial system. It might sound strange to abstract physical space away like this, but I strongly recommend you do it.
When Through the Ages was released, it was touted as being "just like the computer game Civilization... but without a map". I was as incredulous as anyone, but it really does work.
Spatial systems typically require a board, and pieces, which adds significantly to a game's component costs. Spatial systems can also add vast rules complexity and information overload.
If you do want to use a spatial system, consider using a simpler spatial system, such as 1D (a line or loop), rather than a full 2D one. A 1D spatial system is still a significant game component.
Radlands has a fairly simple spatial system. You play cards into the table. These are in a grid of nine. The location of the columns doesn't matter, but in each column, the cards in front protect the cards behind. It's three very small 1D spatial systems.
A very common 1D system is the "card row". Players can buy cards from the card row, but the cost of a card is determined by its position in the row. The cards at the start of the row are cheap or free, while those at the top are most expensive. When a card is bought, everything above it moves down, and a new card is added to the end. This keeps the prices of cards moving, so players constantly have to evaluate when a card is cheap enough to buy.
In Boss Monster, players build a 1D dungeon. It's a line of Room cards. The enemy attacks the dungeon, starting at one end, and progresses through the rooms in order (and hopefully not right to the end.)
A 2D spatial system is just a grid (or other pattern) as in Cluedo or Scrabble.
Most 2D games involve movement, where one or many agents move around the board.
In many 2D movement games, access is too limited, and the game is extremely slow. This problem is worst when a player has a single "character" or other piece, that moves around the board. I've seen designers avoid this problem, by increasing players' movement speed across the board. However, this often means that the player can access lots of things, but makes the spatial nature of the board irrelevant, as the player can reach almost any location they like.
In one of my prototypes, players realistically moved around a town full of interesting and thematic spaces. They could move a few spaces at once.
I never understood why this game wasn't good, but later, I realised the spatial system had crippled the players' access. They couldn't do what they wanted. Despite it being very thematic and interesting, the spatial board was just serving as a way to greatly limit the players' ability to do things.
This system also reduced the pace of the game to a crawl. Players wanted to do something, but had to spend four turns walking across the board, to get there.
You will likely also need to include rules for "range" in your game. Even if done simply, this can be complex, and create work. I suggest "range" be limited to two spaces away, if you must have it. Anything more, and players can't work it out easily enough.
To create proper access on a 2D board, you can simply have a large number of agents per player. War games tend to do this.
Of course, you can have a very small board.
In Santorini, the board is only 5x5, and each player has two movable workers.
Even with multiple movable agents, they'll likely need to start very spread out, or the game will begin with five turns of "going for a walk".
Chess, with sixteen pieces per player, has significant access limitation at the start of the game, but this phase is brief, and consequential.
Give the players a reason to move around the board. I want to have to survey the board, and factor my location into my plans. That's interesting.
I've played many prototypes where I just move to the enemy, and then stay there, thus making the spatial system irrelevant.
Harder still, you want the player to keep moving around the board. Why won't they just stay in one spot? What stops them using a particular area repeatedly? These are hard problems.
Placement is a much safer way to use a 2D board. This means placing more and more pieces onto the board, rather than moving them around.
In Blokus, players place Tetris-shaped pieces on a grid, but they can (and must) connect each subsequent piece to the corner of a piece they placed previously. The player who gets rid of the most pieces before the board clogs up, is the winner. Blokus uses a full 2D system, but is a very light game.
Placement only makes thematic sense for a minority of themes, but it's vastly easier to design around, mechanically. It also tends to have very good access.
Placement allows full access to the board, and it doesn't require (often complex) movement or range rules. The shapes and spatial relationships formed by these pieces can be made to matter, and can be the core of the game. Fitting jigsaw pieces together can be fun.
There are some great medium-light games that combine object placement with a simple scoring system.
2D placement is also a kind of accumulation, which is good for games.
If you have a 2D spatial system, then the game is about your spatial system. Don't consider it to be some minor feature.
I strongly suggest almost everyone avoid spatial movement systems.
My attempts have all failed, and I've been designing games for many years. If you have to make a "map" or landscape as your board, don't make it spatial. Just let the player go anywhere on their turn.
You give the player their own tableau of options, or lots of cards. They have plenty of things to do, and their position on the board is of very low importance. This makes for a strange kind of a game, but it can work. I call this the travelling musician — he can play his music wherever he is.
In Clank! in Space, you move around a spaceship. However, there are only a few types of rooms. This means you can probably get to the kind of room you're looking for fairly easily. The whole game arc is a voyage into the depths of the ship, and then out again, which forces players to keep moving. The focus of the game is the deck-builder part. After you move, you buy new cards for your deck. This is completely unrelated to where you are in the spaceship. All together, this makes this 2d movement game work.