I see Tokaido accomodates from 2 to 5 players. I am wondering wether there is aspects to the game that is problematic or less entertaining with only 2 players?
Note: I've played with two players exclusively, so I cannot compare it to 3+ player games.
Tokaido is inherently not a highly competitive game. You stroll across Japan taking in the sights, local cuisine, and having minor adventures (making new friends, bathing with monkeys, etc).
The neutral piece offers an element of minor sabotage; whoever is in the lead when it is the neutral piece's turn to move can bump it right in front of where the other player wants to go... alternatively you can just beeline the neutral piece to the inn. But no matter how spiteful you want to be by staying in the lead and controlling the neutral player, you're only shooting yourself in the foot by skipping so many spaces.
Ultimately it's a fun game to play when you don't feel like over-analyzing the game... it's not about "winners" and "losers" and more about which player had the most fulfilling journey.
TL;DR-- The two player rules add an extra element of gameplay through the inclusion of a neutral traveler and the removal of the secondary spaces. (two players can never share a spot on the road except at inns) Personally, I find it enjoyable.
The two-player rules for Tokaido include a "dummy" player, i.e. you play with 3 travellers, but the third one is neutral, moved by whoever is currently in the lead, and is only used for blocking spaces and having some effect on Temple scoring and food choices at inns. This changes the strategy space of the game somewhat (since there is now a small benefit to being further ahead on the road, and the neutral traveller doesn't move to his own benefit but to one player's dis-benefit). Whether that makes the game more or less entertaining is presumably a matter of taste.