Welding schools for welders are available all over the US and worldwide.There are trade schools and community colleges for welders.
For welding engineering, there are universities that offer 4 year and 2 yeardegrees. There are a few who offer Masters and Ph.D level degrees also.

Links (Trade Schools):
Illinois Welding School, Tulsa Welding School , Hobart Institute , Modern Welding , Lincoln Tech , John Lopez Welding , Knight School ,
Caltrade Welding , Albany Weld School , Advanced Welding Institute ,Four M Welding , Commercial Diving Academy , Lanier Tech ,
Apex Technical , CIT , Oceancorp

Welding Community Colleges:
Pennsylvannia College , Austin Community , Allegheny County , South Seattle , Alabama Southern , Mesa , Pima , Weld-Ed ,
Manchester , Southeast , Spokane , Maryland , Mid-Plains , Wayne , Clark State , Hawkeye (John Deere) , Rogue ,
Terra , Honolulu , Lawson State , Richland , Lane , Coffeyville , Salt Lake , Edison , New River , Wake Tech , Treasure Valley ,
Ivy Tech , Owens , Wallace , Aims , Green River , Monroe , Macomb , Lansing

4yr Colleges/Univsersities :
Ohio State , Ferris State , Letourneau , Cranfield , MIT , Penn State , Colorado School of Mines , Univ of Kentucky