「ような」の意味は、おわかりのように、it seems / it's like です。 旅に出る、は、旅行に出かける、とほぼ同じで、set off on a journeyということです。 二人とも旅に出るような気分で、とは、実際に旅行には行かないけど、そういう気持ちになっている、と言うことです。 たとえば、 （まるで）お姫様にもなったような気分で、思いっきり買い物を楽しんだ。 As if I were a princess, I enjoyed shopping very much. お役にたてば嬉しいです。

Yeah I think you're right. ような+noun has a meaning of either: - A (noun) like (noun) やぎのような顔 (a face like a goat) - A (noun) that/which looks/seems (adjective/verb) 彼女は僕にキスするような顔をしています。(She looked like she was going to kiss me) So I think you are right in your assumption of the meaning of ような。The question here I think is what exactly is meant by 出る。 出るような気分。 In my opinion, I think it with a feeling of leaving. The boys have just left their (town?), they are on the train, watching the landscape change through the window. Their feeling right now is probably a feeling we have all had when we are leaving our hometown, maybe on the airplane by ourselves, looking out the window and pondering everything at once but nothing in particular. So I think it refers to this feeling, the feeling of leaving.

「ーような」 like, similar to the two of them, even while travelling, with feeling similar to wanting to leave....