Which sentences tell us that Framton did not paticularly want to be in the house?
The second paragraph in "The Open Window" contains the most important indication that Framton Nuttel did not particularly want to be in this house.
Privately he doubted more than ever whether these formal visits on a succession of total strangers would do much towards helping the nerve cure which he was supposed to be undergoing.
Nuttel has already been making formal visits at the homes of other total strangers, so he is developing an aversion to the whole ritual. Since his dislike of what his sister has forced him to do has been building up with his experiences in the country, we can assume that he feels the most dislike for this latest visit to the Sappletons. The fact that he is forced to make conversation with a not overly friendly young girl does not bode well for this visit. She tells him he will have to put up with her, which implies that she is also putting up with him.
The only other obvious indication that Nuttel does not particularly want to be in this house is to be found a few lines further down after Vera asks him if he knows many people in the area. He answers:
"Hardly a soul," said Framton. "My sister was staying here, at the rectory, you know, some four years ago, and she gave me letters of introduction to some of the people here."
He made the last statement in a tone of distinct regret.
He regrets that he consented to take those letters of introduction and put them to use. So far his experiences have been disappointing. He cannot be expecting anything different here. No doubt his disappointing experiences have been partly his own fault. He is boring. Mrs. Sappleton sums him up to her husband when the men return from their hunting through the open window.
"A most extraordinary man, a Mr. Nuttel," said Mrs. Sappleton; "could only talk about his illnesses..."
She could hardly conceal her boredom while she was talking to Nuttel before the hunters returned. Nuttel has told her all about what his doctors have prescribed and:
"On the matter of diet they are not so much in agreement," he continued.
"No?" said Mrs. Sappleton, in a voice which only replaced a yawn at the last moment.
It seems like an unpleasant duty for Nuttel to be going around to strangers' houses with letters of introduction from a woman who was only visiting the area four years ago and apparently never got to know any of the inhabitants very well. We can sympathize with Nuttel, and we can also sympathize with all the people on whom he is intruding. The letter of introduction he uses to meet the Sappletons will undoubtedly be the last such letter he will present. The rest will go into the fireplace.