I feel like going on a trip.

Literal

Travel [to-に] go-out [desire-たい] feeling [subject-が] does.

~気がする (to feel like / to have a feeling that) expresses a subjective impression or desire. 出かけたい気がする = 'I have the feeling of wanting to go out.' Softer and more tentative than simply saying 出かけたい (I want to go out).