I work in a start up company and I am not happy with the working atmosphere here. This is my 7th month in this company and I need to quit. By the time I have to find another job for myself. Here we have a tight schedule that its not easy to get leave. So what would be best reason to take leave for one week so that I can attend interviews.
Many companies are willing to work with your schedule so that you can do some interviews over an extended lunch, after hours, early in the morning before your regular job starts.
You aren't going to be interviewing all day every day for a week so skip taking a week. Fill in individual 2 hour blocks at the beginning or end of days (I recommend end) labeled personal appointment. If you have the time accrued, they have no business asking the nature of the appointment so long as you identify it as personal.
Don't make up excuses or lies because eventually something will catch up to you. Simply leave it unidentified. Job interviews could stretch out for a month or more, so plan ahead and make the time count.
Your reason: "Personal business". At most employers I'm familiar with, that's sufficient. You may not be paid for that time (which is entirely reasonable), but they don't have any need to know what you're using it for, and not saying is always better than lying.
Yes I agree that you should just take an extended lunch hour or something. Say that you have to take an extra lunch break because of personal matters. If they ask what, just say you have to take care of some business. That isn't really "lying" per se. If they continue to press, then at that time you'd probably need to say something.
Now the worst thing you can do, in my opinion, is use company property to conduct the interview or setting up interviews. You should do that on your own time, not on company's time.
However, if you come to work in a suit and all dressed up, you're going to draw suspicion. The thing is in any professional environment, they shouldn't get that upset that you are going to interviews and they should view you updating your resume/portfolio as a common thing. You may be surprised to learn that they might counter offer you to stay or even attempt to give you a raise if they know you are trying to leave and they like you.