“今天早上我到Kroger去了” is correct.In past tense,character “了” is usually placed behind the verb or behind the whole sentence.When placed behind the whole sentence,it stresses that all the activities in the sentence have been done.Eg.:1.我去学校了。2.他昨天已经做完作业了。But when the sentence is in negative form which contains the character “没”,do remember that “了” mustn't be used.Eg. “你没擦黑板了” is a wrong sentence.Unless “没”or“没有” is used as an independent predicate(no other verbs in the whole sentence),which means "none\run out",then you can add “了” to it.Eg. “汽油没了” and “教室里已经没有人了” are both correct sentences.
When “了” is used behind a verb,then the object in most case have adjunct words in front of it.This form stresses that this verb has done.Eg.“我吃了一碗面。” “一碗” is an adjunct word.“他们看了一场精彩的电影。” “一场精彩的电影” is also the adjunct words.When two or more verbs show up at the same time,attach “了” to the last verb.Eg.“我去北京参加了公司的会议”。So your question can also be spoken as “今天早上我去了Kroger。”
In fact,“了” has even much more usages,you can find them out in your future learning :)
PS:Kroger is “克罗格” in Chinese.