Your question asked whether you could end a sentence with "used to". The answer is "yes", especially in informal speech. However your use of "have" is in error.
You have to find a new shop when you are no longer able to go to the shop that you used to.
Many strict grammarians in the past considered it wrong to end a sentence with a preposition. It was the kind of prescriptive 'rule' that makes little sense in reality. But in formal contexts it may still be advisable to avoid ending sentences with prepositions if you can do so without creating something cumbersome.
Adding "go" to the end of the sentence as you have done, does not "fix" the sentence, but introduces an error. "Go" has to have its preposition "to" somewhere, even if you move it away from the end of the sentence. In your sentence "to" has been lost.
To avoid ending the sentence in a preposition you would need to say this:
You have to find a new shop when you are no longer able to go to the shop to which you used to go.
When avoiding ending sentences with prepositions, the construction "to which, from which, on which, under which ..." (etc) is usually required.
As the oft cited, technically misleading, and certainly apocryphal statement made by Winston Churchill* makes clear:
This is the sort of bloody nonsense up with which I will not put.
insisting on not ending sentences in prepositions can get you into cumbersome mess.
(*Quoting Churchill, like Dr Johnson, is the last refuge of the scoundrel.)