I like octagonal grids. Sure, you have to have your game in hyperbolic space, but you can have accurate movement in 8 directions. Your players will just have to deal with parallel lines diverging, there being unique things like pseudocycles, horocycles, circles with a circumference that grows exponentially with increasing radius, etc. Sadly such geometry isn't supported by any tabletop software I'm familiar with, and crocheting a game board of sufficient size takes a very long time.
The biggest issue with adapting it to multiplayer (tabletop) games would be splitting the party. If the party splits, finding a path back together (without just backtracking) can become effectively impossible. Visualizing the spatial relationship between widely spaced points in hyperbolic space is also really hard.
