If you don't care what you see it is great, and you might get to see something you might not have otherwise picked but that you turn out to absolutely love. We used to go to NY every summer. We would buy tickets to one show we really wanted to see before our trip, and then when there we would go to the 1/2 price TKTS and get tickets to something else. We saw some great shows that way, and sometimes we got pretty good seats too! As someone else said, the tickets are not always 1/2 price, sometimes the discounts are smaller- it just depends on the show.
The line at the times square location can be extremely long. Nala you are right about getting out there an hour early. On Sundays, I believe the Times Square location is the only one open, so if that is your day you are good with that location. If I remember correctly, they do open at 11:00 on Sunday; however, they only sell tickets to the matinees at that time. I do not think that they start selling tickets to the evening performances until 3:00 p.m. If it were me, I would go in the morning and shoot for a matinee.
For days other than Sunday, If you can get to the South Street Seaport Booth, that is your best bet. Check the TKTS website, but usually the South Street Seaport Booth has a shorter line and it opens at 11:00 a.m. At that time, it will sell tickets for that night, and for the matinee the NEXT day.
For evening performances, the Times Square booth is usually not open until 3:00 p.m. (I think on Tuesday it is 2:00 p.m.). On Wednesday and Saturdays, the booth opens at 10:00 a.m. to sell matinee performances for THAT day , BUT you can not buy tickets for the evening performances at that time. You have to wait until 3:00 p.m. (2:00 on Tuesday) to get the tickets for that evening.
That means if you can get to South Street, you will have a much better choice of tickets. For matinee, you will get tickets a full day before they go on sale at the Times Square booth. For that evening, you will get them several hours before they go on sale at the times square booth.
I would also suggest trying BroadwayBox.com before you leave for your trip. Their discounts can be just as good as TKTS without having to wait in line!