Technically the ATP season ends some time after the U.S. Open so it is the last Grand Slam Tournament played, but in the next season the Australian Open is the next Grand Slam tournament played after the US Open.
There are four grand slams in a year
The first one is the Australian open and usually takes place during the last two week of January and is played on hard courtThe Second grand slam is on clay court and is the French Open also known as Roland Garros. This usually takes place around the last week of May and the first week of June. (All grand slams are two weeks long)The Third Grand Slam is at Wimbledon and takes place the last week of June and first week of July and this is played on grass courts.The last grand slam of the year is the U.S. Open and takes place around the last week of August and first week of September and this is also played on hard courts.
There are tournaments everyday, yet not on the professional tour. The next professional tennis major and minortournaments can be seen on this website.
Tournaments are happening everywhere almost every day of the year!
If the question refers more specifically to the Davis Cup, the 'tournament' is conducted over four weekends, spread out over the year, played in the various countries among the top 16 nations for that year.
The Australian Open is the next open after the U.S. Open. The Australian Open begins play on Monday 16 Jan 2012 to Sunday 29 Jan 2012 (If not delayed.)
Carolinas International Tennis Tournament was created in 1971.
Caversham International Tennis Tournament was created in 2008.
Carolinas International Tennis Tournament ended in 1977.
Ciutat de Barcelona Tennis Tournament ended in 2006.
Smash Court Tennis Pro Tournament was created in 2002.
River Oaks International Tennis Tournament was created in 1931.
Ciutat de Barcelona Tennis Tournament was created in 1993.
Smash Court Tennis Pro Tournament happened in 2002.
A junior tennis open is a competitive tennis tournament for players in the United States 18 years of age and younger.
Toray Pan Pacific Open Tennis Tournament was created in 1984.