If Lord Krishna wanted to stay with Duryodhana's house But why he chosen the Viduar's house? I have heard one notable thing is that Lord Krishna had eaten the dandelion's bread in Vidura's house.
The worship being over, king Duryodhana invited him of Vrishni's race--that foremost of victors--to eat at his house, Kesava, however did not accept the invitation. The Kuru king Duryodhana seated in the midst of the Kurus, in a gentle voice but with deception lurking behind his words, eyeing Karna, and addressing Kesava, then said, 'Why, O Janardana, dost thou not accept ... [source]
Krishna being a good diplomat, at first tried to answer without hurting anyone's sentiments:
The high-souled Govinda ... replied ... 'Envoys, O king, eat and accept worship only after the success of their missions. Therefore, O Bharata, after my mission becomes successful, thou mayest entertain me and my attendants.'
However Duryodhana was adamant on why Krishna shouldn't accept his invitation when there is no war, no hatred and moreover Krishna is helping both the sides. However, this time Krishna chose to discard his politeness to avoid further arguments and replied:
'One taketh another's food when one is in distress. At present, however, O king, thou hast not inspired love in me by any act of thine, nor have I myself been plunged into distress. Without any reason, O king, thou hatest, from the moment of their birth, thy dear and gentle brothers,--the Pandavas--endued with every virtue. This unreasonable hatred of thine for the sons of Pritha ill becometh thee. ... He that hateth them, hateth me; he that loveth them, loveth me. Know that the virtuous Pandavas and my own self have but a common soul. He, who, following the impulses of lust and wrath, and from darkness of soul, hateth and seeketh to injure one that is possessed of every good quality, is regarded as the vilest of men. ... Defiled by wickedness, all this food, therefore, deserveth not to be eaten by me. The food supplied by Vidura alone, should, I think, be eaten by me. ...'
This conversation was kind of insult for Duryodhana, who was not used to listen anything against his own wishes.
Another idea behind not having or having certain food from certain person, could be to avoid acquiring their qualities or being indebted to their offerings.
Krishna was visiting Hastinapura as a messenger of peace. The peace that would save a lot of lives from the war of Kurukshetra. When the Kauravas get to know that Lord Krishna is coming they have an internal discussion on how well can they impress Krishna. Dritharashtra and his sons do not understand Vidhura's or Bhishma's explanation that one cannot impress the lord without love. One cannot impress the Lord with gifts and luxury but with love and faith. With truth and ethics.
When Krishna arrives,
Dritharashtra: “Dushyasan, take Lord Krishna to your Bhavan (house) and serve him dinner. Take good care of him. He will be tired due to the journey.”
Duryodhana: “No no, first I'll take Lord Krishna to my place. Let him have dinner there and then Dushyasana may take him to his house.”
Krishna rejects the offer and says: “One can eat in friends' place or in host's place. But Duryodhana or the rest of the Kauravas are neither hosting me nor am I their friend. Therefore I'll stay at Mahatma Vidhura's home.”
Why Mahatma Vidhura's home? He was one person in Hastinapura who was truthful. He was one person who was on the side of Dharma.
Krishna needs no invitation to come to your place if you have unconditional love and devotion toward him. Vidhura did not try or think of impressing Krishna and that's what impressed Him.