Nice game, art is maybe a bit noisy and hard to read at some points. Tile selection is a bit too greedy and targets full next tile (position+fixed size) which makes for a “long” distance once moving into the next tile that gets shorter until you hit the next tile (kind of jumpy…) and I might maybe have gone for mid-tile checks to balance that distance a bit better. Music can be a bit too loud… a lower volume for the same tune probably will not be as intrusive. Did not get too far, and did not figure out how to interact with the stores… Anyway, still a good concept, requiring some polishing, but is a very good starting point!
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My guess is that you are calculating which tile you are on and selecting the next tile (from the behaviour) so you take your x and your y, divide by tile width or height and add 1 full tile (or take one if looking up or left)… Maybe I am just wild guessing, but that sounds like it… and I think your control point for the sprite is in the center, not one corner.
One think you could try is check against the corner that is opposite to the movement direction and that will make you be halfway into the tile before jumping into the next (well check 1 px off the exact corner or you will hit your current tile when fully tile aligned), That’s what came to my mind when I wrote the comment. Not sure if that will help/fix your issue though.