I have entities with move as a member function, and it basically delegates to the map to do the physical moving, but then the entity can override the virtual move function to do something before or after the move, while if you have a monolithic move function for the map, handling pre-post ops on a type by type basis gets nuts.
I don't think having 'move' owned by the map is wrong per se but I think you can make a stronger argument for something like eclectocrat's design here.
The sky won't fall down whichever way you do it, unless the codebase or the game gets a lot more complicated.
First off why do you need lots of different pre and post steps for movement? I would be quite worried if that happened because it means you derive a new critter class just to get a new kind of movement. If your game does have a lot of very different forms of movement you should be abstracting that out of the critter anyway, e.g. into a hierarchy of movement objects. (I'm assuming that like in most games critters are not uniquely determined by their style of movement.)
If you don't factor it out and you have another method/behaviour on the critter that can vary, an attack() method say, then you could be for a right pain in arse. You only need 3 types of movement and 3 types of attack to lead to 9 different classes you could have to write. Of course you could make a faustian pact and use multiple inheritance but possibly reduce the amount of code you write at the cost of you sanity.
It would be easier to factor both movement and attacking out into their own objects or hierarchies (thereby turning a N*M problem into an N+M problem). This also has the nice side effect of being far easier to make data driven (so new critter types can be added without writing code).
The oft quoted slogan of 'favour composition over inheritance' essentially means that the ideal number of critter classes is one. It's also motivated by very similar arguments to those presented above.
So if you have a small numbers of methods/verbs you won't really feel the pain but I've worked on RTSs where the number of combinations got quite large and the 'critter move' solution writ large led to loads of issues. Once we changed to the compositional system (and put 'move in the map') for the subsequent game it all went a lot more smoothly.