They are called Advanced Dining Reservations (ADRs) now. ADRs can be made up to 180 days in advance, so that would explain why things are all booked up 2 - 3 months in advance. If you are going during a busy time of the year, it is not surprising that nothing is available. Try to be more flexible on meal times (say, dinner at 5:00 or 8:30, rather than 6:30; things like that) and you may have more luck. If you can't get ADRs for a specific place at a specific time, you are not likely to have better luck just walking up to a place and hoping to get a table.