Which sentence is correct?
1. Did you like the hotel where you stayed?
2. Did you like the hotel where you stayed at?
I am curious as to whether to use at or not.
The first one is correct.
Do you like the hotel where you stayed?
If you didn't have the "where," however, you could get away with including the "at."
Do you like the hotel you stayed at?
That has a dangling participle, and would more grammatically correctly be phrased
Do you like the hotel at which you stayed?
Although that's way more formal than how anyone would probably speak in real life.
I think the difference between the two you said becomes a bit more evident when you change it around a bit.
Where did you say last night?
That sounds a lot more comfortable than its equivalent
Where did you stay at last night?
Of course, you could also say:
Which hotel did you stay at last night?
And that would be reasonable.
It's ultimately just a choice between "where" and "at which."
1.Did you like the hotel where you stayed?
This is correct. The relative pronoun where has the meaning of at/in/to which.
2.Did you like the hotel where you stayed at?
As the where contains within itself the idea of at, the at in your sentence is redundant, and the sentence is incorrect. You can say:
3. Did you like the hotel you stayed at/in?
4. Did you like the hotel at/in which you stayed?
No. 4 is rather formal.