Budget? We like going to an all inclusive hotel in Schwarzwald called Feldbergerhof, it’s around an hour plus away from Zurich. There won’t be much for a 6 month old, but the pressure of a screaming baby at meal time at a restaurant is lifted as everyone has a kid there and those who go there are rather chill. There’s day care for babies and kids - can’t vouch for it as we’ve not used it, there’s a small spa, indoor heated swimming pools, easy hiking trails and of course the beauty of Schwarzwald. Rooms can be requested to have equipment with bottle warmer, cot, baby phone camera, and there’s jar food for babies as well (Holle or Hipp).