rasta
On easy mode you get the timeturner item that allows you to progress you day as many times as you want, but on any other modes the only way to progress the day is quests, and then one more day from the bunnyboi
As for vacation, that depends on your question. Did you ask if it will give you extra days to increase your girls affection? Then no, vacations doesn't increase their affection
Do you mean daily income, spell learning progress and EXP from the daily dungeons? Then yeah the sooner the better, do it right and you can actually gain more money from daily income than the actual cost of the vacation